A178235 a(n) = 2*(n+2)!*(zeta(-2*n)-zeta(-n)), zeta(n) the Riemann zeta function.

0, 1, 0, -2, 0, 40, 0, -3024, 0, 604800, 0, -262690560, 0, 217945728000, 0, -315323879270400, 0, 742997162299392000, 0, -2703345607134653644800, 0, 14552624755991316234240000, 0, -111913707637423660385894400000, 0

Offset

0,4

Comments

Old name was: A polynomial expansion: p(x,t)=-Exp[t]*(-1 + Exp[x])/(-1 + Exp[t]).

The expansion is the solution for integer q of: q*Exp[x*t]/(q - 1 + Exp[x]) - Exp[t*(1 + x)] = 0. (See the Mathematica program.) That result is a generalized Euler number in q as a Pascal expansion. For higher Sierpinski-Pascal levels (Eulerian and MacMahon) this results in polynomials.

For n >= 9, a(n) is divisible by 2*10^(floor(n/5)-1). - G. C. Greubel, Nov 06 2015

Links

G. C. Greubel, Table of n, a(n) for n = 0..200

Maple

A178235 := n -> 2*(n+2)!*(Zeta(-2*n)-Zeta(-n)); seq(A178235(n), n=0..24); # Peter Luschny, Jul 14 2013

Mathematica

p[t_] = -Exp[t]*(-1 + Exp[x])/(-1 + Exp[t]); Table[ FullSimplify[ExpandAll[(2*(n + 2)!n!/(1 - Exp[x]))*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], {n, 0, 30}]

Crossrefs

Sequence in context: A337817 A120489 A145576 * A214447 A357541 A230888

Adjacent sequences: A178232 A178233 A178234 * A178236 A178237 A178238

Keyword

sign

Author

Roger L. Bagula, May 23 2010

Extensions

Edited, new name and a(0) changed to 0 by Peter Luschny, Jul 14 2013

Status

approved