Measures of Hexanomials P(a,2a-1)

Measures of polynomials of the form

Pa,2a-1(x,y) = ((1-xa) + (1-x2a-1)y + xa-1(1-xa)y2)/(1-x)
with 0 < a <= 100. Indicated by P(a,2a-1).

      a   2a-1   M(P(a,2a-1))
      1    1     1.000000000000000000000000000
      2    3     1.255433866266608745687508172
      3    5     1.315692702986641093482764106
      4    7     1.339999921738183533201441401
      5    9     1.352468062518860296095239367
      6   11     1.359811775281940502089703661
      7   13     1.364545985789915136670760332
      8   15     1.367798858011715774019399184
      9   17     1.370142554532182727235247515
     10   19     1.371894385113041081623151170
     11   21     1.373242742246592145583980077
     12   23     1.374305664495906269208700919
     13   25     1.375160407623480559612119931
     14   27     1.375859393698226885530629617
     15   29     1.376439290909602928280072219
     16   31     1.376926421554123769867314596
     17   33     1.377340108985907543018051134
     18   35     1.377694818474538877024859228
     19   37     1.378001566440883390309107399
     20   39     1.378268871753536539978127987
     21   41     1.378503412370746213641378984
     22   43     1.378710487692059767892314265
     23   45     1.378894349964817175210222905
     24   47     1.379058445685084178001023080
     25   49     1.379205594023118005659136138
     26   51     1.379338120468254410288873733
     27   53     1.379457958158239113170182420
     28   55     1.379566725571034301620287366
     29   57     1.379665786710481755412914261
     30   59     1.379756298177173055846706584
     31   61     1.379839246309400156768449220
     32   63     1.379915476731095315960361131
     33   65     1.379985718040128376530625568
     34   67     1.380050600935693040841773728
     35   69     1.380110673767072382496617937
     36   71     1.380166415253318264623963935
     37   73     1.380218244950530154707622307
     38   75     1.380266531913897430972689059
     39   77     1.380311601903789751372946529
     40   79     1.380353743410619786136026485
     41   81     1.380393212715976367464675593
     42   83     1.380430238163289900781332892
     43   85     1.380465023776865438902633886
     44   87     1.380497752341154627283122884
     45   89     1.380528588030889412554880137
     46   91     1.380557678665859152646988281
     47   93     1.380585157650690760438367335
     48   95     1.380611145649238201360759479
     49   97     1.380635752034529117136259342
     50   99     1.380659076148211007721099374
     51  101     1.380681208397745577120791410
     52  103     1.380702231214951642174307637
     53  105     1.380722219895686402458316121
     54  107     1.380741243337318307319520529
     55  109     1.380759364688052984637011202
     56  111     1.380776641920024104165814109
     57  113     1.380793128336271803765635673
     58  115     1.380808873020236864055070641
     59  117     1.380823921235146456302807396
     60  119     1.380838314779614435013931968
     61  121     1.380852092304891285340105657
     62  123     1.380865289598447879711936429
     63  125     1.380877939837940210428550257
     64  127     1.380890073819060447462393874
     65  129     1.380901720160317566211943566
     66  131     1.380912905487395646702098084
     67  133     1.380923654599399211002464499
     68  135     1.380933990619003879703536245
     69  137     1.380943935128279898411291158
     70  139     1.380953508291739622577896282
     71  141     1.380962728967972755863180490
     72  143     1.380971614811070734209114758
     73  145     1.380980182362900533085430150
     74  147     1.380988447137165309738569601
     75  149     1.380996423696082105004577168
     76  151     1.381004125720413140639636013
     77  153     1.381011566073505205773202866
     78  155     1.381018756859919652183901324
     79  157     1.381025709479172265765000090
     80  159     1.381032434675046598598453939
     81  161     1.381038942580895244806875157
     82  163     1.381045242761300175415569870
     83  165     1.381051344250424882665674435
     84  167     1.381057255587357092948608384
     85  169     1.381062984848710645836779729
     86  171     1.381068539678728333785542168
     87  173     1.381073927317103644795376766
     88  175     1.381079154624718094130792270
     89  177     1.381084228107471862658351113
     90  179     1.381089153938368509706256200
     91  181     1.381093937977999362953284447
     92  183     1.381098585793559601624002404
     93  185     1.381103102676515862618492349
     94  187     1.381107493659034254664433431
     95  189     1.381111763529267824856482583
     96  191     1.381115916845593663423056599
     97  193     1.381119957949881849125491291
     98  195     1.381123890979871234890622865
     99  197     1.381127719880720567690182162
    100  199     1.381131448415797554549405765


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mimossinghoff "at" davidson "dot" edu
July 12, 2002.