A009634 E.g.f. tan(x*cosh(x)), zeros omitted.

1, 5, 81, 3429, 238273, 25669093, 3923627345, 807194393477, 215176572950017, 72120516857475141, 29686285367774651089, 14721686852776234894885, 8656857857596485141973441, 5955926696414663185424979749

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Programs

Mathematica

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 *)

Maxima

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

PARI

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 */

Formula

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

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Name corrected by Joerg Arndt, Apr 23 2011

Previous Mathematica program replaced by Harvey P. Dale, Sep 06 2017