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A147563 A scaled Bernstein-type polynomial set based on A008292 Eulerian numbers: p(x,n)=4*Sum[A008292[[n]][[m + 1]]*(x/2)^(n - m - 1)*(1 - x/2)^m, {m, 0, n - 1}] 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..52.

FORMULA

p(x,n)=4*Sum[A008292[[n]][[m + 1]]*(x/2)^(n - m - 1)*(1 - x/2)^m, {m, 0, n - 1}]; t(n,m)=coefficients(t(n,m)).

EXAMPLE

{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}

MATHEMATICA

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[%]

CROSSREFS

Sequence in context: A177229 A046595 A046587 * A136213 A088848 A088849

Adjacent sequences:  A147560 A147561 A147562 * A147564 A147565 A147566

KEYWORD

sign

AUTHOR

Roger L. Bagula, Nov 07 2008

STATUS

approved

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Last modified October 16 19:00 EDT 2018. Contains 316271 sequences. (Running on oeis4.)