login
E.g.f. tanh(sin(x)*exp(x)).
1

%I #14 Apr 02 2017 12:25:16

%S 0,1,2,0,-24,-148,-248,5488,73024,346768,-3749728,-100273536,

%T -922745472,4147334336,283697686144,4362058183936,4465927211008,

%U -1382047649378048,-33554250522144256,-226963355560685568,10084981854738991104

%N E.g.f. tanh(sin(x)*exp(x)).

%F a(n)=sum(m=1..n, ((sum(k=1..m, (-1)^(k+1)*k!*2^(1-k)*stirling2(m,k)))*sum(j=0..(n-m)/2, binomial(n,2*j+m)*(m^(n-2*j-m)*sum(i=0..m/2, (2*i-m)^(2*j+m)*(-1)^(m+j-i)*binomial(m,i))) ))/(m!)). - _Vladimir Kruchinin_, Jun 30 2011

%o (Maxima)

%o a(n):=sum(((sum((-1)^(k+1)*k!*2^(1-k)*stirling2(m,k),k,1,m))*sum(binomial(n,2*j+m)*(m^(n-2*j-m)*sum((2*i-m)^(2*j+m)*(-1)^(m+j-i)*binomial(m,i),i,0,m/2)),j,0,(n-m)/2 ))/(m!),m,1,n); /* _Vladimir Kruchinin_ Jun 30 2011 */

%K sign,easy

%O 0,3

%A _R. H. Hardin_

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