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A171692 Triangle read by rows: absolute values of odd-numbered rows of A159041. 8
1, 1, 10, 1, 1, 56, 246, 56, 1, 1, 246, 4047, 11572, 4047, 246, 1, 1, 1012, 46828, 408364, 901990, 408364, 46828, 1012, 1, 1, 4082, 474189, 9713496, 56604978, 105907308, 56604978, 9713496, 474189, 4082, 1, 1, 16368, 4520946 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

Row sums are: {1, 12, 360, 20160, 1814400, ...}.

LINKS

Table of n, a(n) for n=2..40.

FORMULA

Infinite sum on a 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*y))*n!

EXAMPLE

{1},

{1, 10, 1},

{1, 56, 246, 56, 1},

{1, 246, 4047, 11572, 4047, 246, 1},

{1, 1012, 46828, 408364, 901990, 408364, 46828, 1012, 1}

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

Flatten[a]

CROSSREFS

Cf. A008292, A159041, A060187.

Sequence in context: A157629 A154336 A174109 * A152971 A142459 A157641

Adjacent sequences:  A171689 A171690 A171691 * A171693 A171694 A171695

KEYWORD

nonn,tabf

AUTHOR

Roger L. Bagula, Dec 15 2009

EXTENSIONS

Edited by N. J. A. Sloane, May 10 2013

More terms from Jean-Fran├žois Alcover, Feb 14 2014

STATUS

approved

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Last modified February 27 06:33 EST 2020. Contains 332299 sequences. (Running on oeis4.)