A009634 - OEIS

%I #29 Sep 06 2017 17:47:39

%S 1,5,81,3429,238273,25669093,3923627345,807194393477,215176572950017,

%T 72120516857475141,29686285367774651089,14721686852776234894885,

%U 8656857857596485141973441,5955926696414663185424979749

%N E.g.f. tan(x*cosh(x)), zeros omitted.

%F a(n) = b(2*n+1) where b(n) = Sum_{k=1..n} (binomial(n,k)*(((-1)^(k-1)+1)*(Sum_{i=0..k} (k-2*i)^(n-k)*binomial(k,i))*Sum_{j=1..k} j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k,j))/(2^k)). - _Vladimir Kruchinin_, Apr 21 2011

%t With[{nn=30},Take[CoefficientList[Series[Tan[Cosh[x]*x],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Sep 06 2017 *)

%o (Maxima)

%o a(n):=b(2*n+1);

%o b(n):=sum(binomial(n,k)*(((-1)^(k-1)+1)*(sum((k-2*i)^(n-k)*binomial(k,i),i,0,k))*sum(j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k,j),j,1,k))/(2^k),k,1,n); /* _Vladimir Kruchinin_, Apr 21 2011 */

%o (PARI)

%o a(n)={n=2*n+1;sum(k=1,n, binomial(n,k)*(((-1)^(k-1)+1)*(sum(i=0,k, (k-2*i)^(n-k)*binomial(k,i)))*sum(j=1,k, j!*2^(k-j-1)*(-1)^((k+1)/2+j)* stirling(k,j,2)))/(2^k));} /* Kruchinin's formula; _Joerg Arndt_, Apr 22 2011 */

%K nonn

%O 0,2

%A _R. H. Hardin_

%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997

%E Name corrected by _Joerg Arndt_, Apr 23 2011

%E Previous Mathematica program replaced by _Harvey P. Dale_, Sep 06 2017