%I A147563
%S A147563 4,4,4,4,2,4,16,8,4,44,6,16,4,4,104,84,136,34,4,228,606,584,24,
%T A147563 102,17,4,480,2832,1088,2208,1488,248,4,988,11122,5536,20840,8896,
%U A147563 832,992,124,4,2008,39772,74296,118190,2144,51952,22112,2764,4,4052
%V A147563 4,4,4,4,-2,4,16,-8,4,44,-6,-16,4,4,104,84,-136,34,4,228,606,-584,-24,
%W A147563 102,-17,4,480,2832,-1088,-2208,1488,-248,4,988,11122,5536,-20840,8896,
%X A147563 832,-992,124,4,2008,39772,74296,-118190,-2144,51952,-22112,2764,4,4052
%N A147563 A scaled Bernstein-type polynomial set based on A008292 Eulerian numbers: 
               p(x,n)=4*Sum[A0008292[[n]][[m + 1]]*(x/2)^(n - m - 1)*(1 - x/2)^m, 
               {m, 0, n - 1}]
%C A147563 The row sums are: {4, 4, 6, 12, 30, 90, 315, 1260, 5670, 28350, 155925,
               ...}. The Eulerian number scaling is based on the quadratic Sierpinski 
               number: (1,2*k,1}: to give a Bernstein Sierpinski probability scale 
               of: p=x/2*(k-1). Here k=2 so k-1 is 2; for Pascal it is k=1 or 2^0.
%F A147563 p(x,n)=4*Sum[A0008292[[n]][[m + 1]]*(x/2)^(n - m - 1)*(1 - x/2)^m, {m, 
               0, n - 1}]; t(n,m)=coefficients(t(n,m)).
%e A147563 {4}, {4}, {4, 4, -2}, {4, 16, -8}, {4, 44, -6, -16, 4}, {4, 104, 84, 
               -136, 34}, {4, 228, 606, -584, -24, 102, -17}, {4, 480, 2832, -1088, 
               -2208, 1488, -248}, {4, 988, 11122, 5536, -20840, 8896, 832, -992, 
               124}, {4, 2008,39772, 74296, -118190, -2144, 51952, -22112, 2764}, 
               {4, 4052, 134358, 527784, -395820, -590322, 655923, -172608, -19884, 
               13820, -1382}
%t A147563 p[x_, n_] = (1 - x)^(n + 1)*PolyLog[ -n, x]/x; a = Table[CoefficientList[FullSimplify[ExpandAll[p[x, 
               n]]], x], {n, 1, 11}]; Table[CoefficientList[FullSimplify[ExpandAll[4*Sum[a[[n]][[m 
               + 1]]*(x/2)^(n - m - 1)*(1 - x/2)^m, {m, 0, n - 1}]]], x], {n, 1, 
               11}]; Flatten[%]
%Y A147563 Sequence in context: A074803 A046595 A046587 this_sequence A136213 A088848 
               A088849
%Y A147563 Adjacent sequences: A147560 A147561 A147562 this_sequence A147564 A147565 
               A147566
%K A147563 sign
%O A147563 1,1
%A A147563 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 07 2008