A009277 E.g.f. exp(tanh(x)^2) (even powers only).

1, 2, -4, -88, 4496, -155488, 675776, 903834752, -178181918464, 26154843525632, -2632795710260224, -207121926659381248, 274561534481040183296, -132684091405061956722688, 50873850498309673207709696

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..235

Crossrefs

Cf. A000182, A354425.

Programs

Mathematica

nmax = 20; Table[(CoefficientList[Series[Exp[Tanh[x]^2], {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[k]], {k, 1, 2*nmax, 2}] (* Vaclav Kotesovec, May 27 2022 *)
With[{nn=30},Take[CoefficientList[Series[Exp[Tanh[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Apr 08 2023 *)

Maxima

a(n):=sum(sum(binomial(k+2*m-1,2*m-1)*(k+2*m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n,k+2*m),k,0,2*n-2*m)/m!,m,1,n); /* Vladimir Kruchinin, Jun 06 2011 */

PARI

x = 'x + O(x^50); select(x->x, Vec(serlaplace(exp(tanh(x)^2)))) \\ Michel Marcus, Apr 01 2017

Formula

a(n) = Sum_{m=1..n} (Sum_{k=0..2*n-2*m} (binomial(k+2*m-1, 2*m-1)*(k+2*m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n, k+2*m))/m!). - Vladimir Kruchinin, Jun 06 2011

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997