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A171693
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Expansion generating function using an infinite sum odd levels:m=0; f(t,y)=Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m*t])*y^x, {x, 0, Infinity}]
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2
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1, -1, 14, -1, 4, -16, 504, -16, 4, -34, 372, 2178, 35288, 2178, 372, -34, 496, -5888, 65728, 749824, 4185760, 749824, 65728, -5888, 496, -11056, 154912, -767856, 23350656, 230640288, 770603712, 230640288, 23350656, -767856, 154912, -11056
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OFFSET
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2,3
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COMMENTS
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Row sums are:
{1, 12, 480, 40320, 5806080, 1277337600,...}.
m=-1 gives MacMahon {1,6,1} A060187.
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LINKS
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Table of n, a(n) for n=2..37.
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FORMULA
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Infinite sum on an generalized Euler numbers/ polynomial scaled generating function:
f(t,y)=Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m*t])*y^x, {x, 0, Infinity}]
Scaling function is:
g(y,n)=((1 - y)^(n + 1)*2^(1 + Floor[(n)/2])/(1 + y))*n!
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EXAMPLE
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{1},
{-1, 14, -1},
{4, -16, 504, -16, 4},
{-34, 372, 2178, 35288, 2178, 372, -34},
{496, -5888, 65728, 749824, 4185760, 749824, 65728, -5888, 496},
{-11056, 154912, -767856, 23350656, 230640288, 770603712, 230640288, 23350656, -767856, 154912, -11056}
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MATHEMATICA
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Clear[m, n, t, x, y, a]
m = 0;
f[t_, y_] = Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m* t])*y^x, {x, 0, Infinity}]
a = Table[ CoefficientList[FullSimplify[ExpandAll[((1 - y)^(n + 1)*2^(1 + Floor[(n)/2])/(1 + y))*n!* SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 1, 11, 2}]
Flatten[a]
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CROSSREFS
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A159041, A060187, A171692
Sequence in context: A040204 A040203 A040205 * A235704 A229199 A040206
Adjacent sequences: A171690 A171691 A171692 * A171694 A171695 A171696
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula, Dec 15 2009
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STATUS
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approved
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