A009276 E..g.f. exp(tanh(x)/exp(x)).

1, 1, -1, -4, 9, 52, -175, -1370, 5985, 60216, -320063, -3929550, 24549745, 354693796, -2543955167, -42233123938, 341610526145, 6404634620016, -57626692351871, -1203767371104790, 11918048043239377, 274395314816604636

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Programs

Mathematica

Exp[ Tanh[ x ]/Exp[ x ] ]
CoefficientList[Series[E^(Tanh[x]/E^x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)

Maxima

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

Formula

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997