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E..g.f. exp(tanh(x)/exp(x)).
1

%I #16 Apr 01 2017 13:58:40

%S 1,1,-1,-4,9,52,-175,-1370,5985,60216,-320063,-3929550,24549745,

%T 354693796,-2543955167,-42233123938,341610526145,6404634620016,

%U -57626692351871,-1203767371104790,11918048043239377,274395314816604636

%N E..g.f. exp(tanh(x)/exp(x)).

%F 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

%t Exp[ Tanh[ x ]/Exp[ x ] ]

%t CoefficientList[Series[E^(Tanh[x]/E^x), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)

%o (Maxima)

%o 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 */

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997