A009798 E.g.f. tanh(sin(x)*cos(x)) (odd powers only).

1, -6, 112, -5488, 451840, -57057792, 10262228992, -2484525168640, 779280513040384, -307370299649556480, 148889329569589362688, -86890528715348714192896, 60129120979379216762011648

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Crossrefs

Cf. A101921.

Programs

Maxima

a(n):=(-1)^n*sum(4^(n-k)/(2*k+1)!*sum((-1)^i*(2*k+1-2*i)^(2*n+1)*binomial(2*k+1, i), i, 0,2*k+1)*(sum(j!*2^(-j)*(-1)^(k+1+j)*stirling2(2*k+1, j), j, 1, 2*k+1)), k, 0, n); /* Vladimir Kruchinin, Jun 28 2011 */

Formula

a(n):=(-1)^n*sum(k=0..n, 4^(n-k)/(2*k+1)!*sum(i=0..2*k+1, (-1)^i*(2*k+1-2*i)^(2*n+1)*binomial(2*k+1, i))*(sum(j=1..2*k+1, j!*2^(-j)*(-1)^(k+1+j)*stirling2(2*k+1, j)))). - Vladimir Kruchinin, Jun 29 2011

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997