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A168524 Coefficients of polynomials:a0 = -7 + 3 c0; b0 = 9 - 5 c0; c0 = 1; p(x,n)=(a0*(x + 1)^n + b0*((1 - x)^( n + 2))Sum[(1 + k)^(n + 1)* x^k, {k, 0, Infinity}])/(2) + c0*2^n* (1 - x)^(1 + n) LerchPhi[ x, -n, 1/2] 1
1, 1, 1, 1, 10, 1, 1, 39, 39, 1, 1, 120, 350, 120, 1, 1, 341, 2266, 2266, 341, 1, 1, 950, 12895, 28340, 12895, 950, 1, 1, 2659, 69201, 290891, 290891, 69201, 2659, 1, 1, 7540, 360772, 2661644, 4987254, 2661644, 360772, 7540, 1, 1, 21681, 1851948, 22618188 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 12, 80, 592, 5216, 56032, 725504, 11047168, 193051136, 3795722752,...}

Linear solution for an {1,39,39,1} cubic level between Pascal, Eulerian and MacMahon numbers.

LINKS

Table of n, a(n) for n=0..48.

EXAMPLE

{1},

{1, 1},

{1, 10, 1},

{1, 39, 39, 1},

{1, 120, 350, 120, 1},

{1, 341, 2266, 2266, 341, 1},

{1, 950, 12895, 28340, 12895, 950, 1},

{1, 2659, 69201, 290891, 290891, 69201, 2659, 1},

{1, 7540, 360772, 2661644, 4987254, 2661644, 360772, 7540, 1},

{1, 21681, 1851948, 22618188, 72033750, 72033750, 22618188, 1851948, 21681, 1},

{1, 63090, 9421325, 182707640, 926399090, 1558540460, 926399090, 182707640, 9421325, 63090, 1}

MATHEMATICA

a0 = -7 + 3 c0; b0 = 9 - 5 c0; c0 = 1;;

p[x_, n_] = (a0*(x + 1)^n + b0*((1 - x)^(n + 2)) Sum[(1 + k)^(n + 1)*x^k, {k, 0, Infinity}])/( 2) + c0*2^n* (1 - x)^(1 + n) LerchPhi[x, -n, 1/2]

Flatten[Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]]

CROSSREFS

Cf. A142458, A142459

Sequence in context: A173045 A176491 A008958 * A157277 A157629 A154336

Adjacent sequences:  A168521 A168522 A168523 * A168525 A168526 A168527

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Nov 28 2009

STATUS

approved

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Last modified February 19 16:24 EST 2020. Contains 332045 sequences. (Running on oeis4.)