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

0,2

Links

Table of n, a(n) for n=0..13.

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

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A009756 A336807 A188419 * A165435 A197443 A337852

Adjacent sequences: A009631 A009632 A009633 * A009635 A009636 A009637

Keyword

nonn

Author

R. H. Hardin

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

Status

approved