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A171693 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}] 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

Row sums are:

{1, 12, 480, 40320, 5806080, 1277337600,...}.

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

LINKS

Table of n, a(n) for n=2..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^(1 + Floor[(n)/2])/(1 + y))*n!

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

A159041, A060187, A171692

Sequence in context: A040204 A040203 A040205 * A235704 A229199 A040206

Adjacent sequences:  A171690 A171691 A171692 * A171694 A171695 A171696

KEYWORD

sign,uned

AUTHOR

Roger L. Bagula, Dec 15 2009

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)