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A171692 Triangle read by rows: absolute values of odd-numbered rows of A159041. 8

%I

%S 1,1,10,1,1,56,246,56,1,1,246,4047,11572,4047,246,1,1,1012,46828,

%T 408364,901990,408364,46828,1012,1,1,4082,474189,9713496,56604978,

%U 105907308,56604978,9713496,474189,4082,1,1,16368,4520946

%N Triangle read by rows: absolute values of odd-numbered rows of A159041.

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

%F Infinite sum on a generalized Euler numbers/ polynomial scaled generating function:

%F f(t,y)=Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m*t])*y^x, {x, 0, Infinity}]

%F Scaling function is g(y,n)=((1 - y)^(n + 1)/(2*y))*n!

%e {1},

%e {1, 10, 1},

%e {1, 56, 246, 56, 1},

%e {1, 246, 4047, 11572, 4047, 246, 1},

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

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

%t m = 0;

%t f[t_, y_] = Sum[2^(m + 1)*Exp[t*x]/(-1 + 2^(m + 1) + Exp[ -2^m* t])*y^x, {x, 0, Infinity}]

%t 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}]

%t Flatten[a]

%Y Cf. A008292, A159041, A060187.

%K nonn,tabf

%O 2,3

%A _Roger L. Bagula_, Dec 15 2009

%E Edited by _N. J. A. Sloane_, May 10 2013

%E More terms from _Jean-Fran├žois Alcover_, Feb 14 2014

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Last modified March 28 04:44 EDT 2020. Contains 333073 sequences. (Running on oeis4.)