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A171694 Expansion generating function using an infinite sum:m=-2; f(t,y)=Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m*t])*y^x, {x, 0, Infinity}] 1
1, 2, 2, 6, 20, 6, 26, 154, 190, 14, 150, 1160, 3428, 1352, 54, 1082, 9174, 50404, 51724, 10434, 62, 9366, 78476, 683962, 1376232, 734122, 65996, 966, 94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786, 1091670, 7562000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are:

{1, 4, 32, 384, 6144, 122880, 2949120, 82575360, 2642411520, 95126814720,

3805072588800,...}.

m=-1 gives MacMahon {1,6,1} A060187.

LINKS

Table of n, a(n) for n=0..37.

FORMULA

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^(2*n)*n!

EXAMPLE

{1},

{2, 2},

{6, 20, 6},

{26, 154, 190, 14},

{150, 1160, 3428, 1352, 54},

{1082, 9174, 50404, 51724, 10434, 62},

{9366, 78476, 683962, 1376232, 734122, 65996, 966},

{94586, 735410, 9096210, 30488714, 32703374, 8931318, 530534, -4786},

{1091670, 7562000, 122859048, 611454960, 1132022084, 653476464, 111158184, 2715536, 71574},

{14174522, 84743566, 1725925480, 11633772184, 33628718668, 34398480388, 12391430344, 1218784120, 31661386, -875938},

{204495126, 1021304852, 25642306094, 216329822576, 907078630988, 1476556625528, 949722706028, 213543053936, 14943309854, 17523092, 12810726}

MATHEMATICA

Clear[m, n, t, x, y, a]

m = -2;

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^(2*n)*n!*SeriesCoefficient[ Series[f[t, y], {t, 0, 30}], n]]], y], {n, 0, 10}]

Flatten[a]

CROSSREFS

A159041, A060187, A171692, A171693

Sequence in context: A176754 A173098 A233113 * A103179 A320932 A225942

Adjacent sequences:  A171691 A171692 A171693 * A171695 A171696 A171697

KEYWORD

sign,uned

AUTHOR

Roger L. Bagula, Dec 15 2009

STATUS

approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)