A009250 E.g.f. exp(tan(x)*sin(x)) (even powers only).

1, 2, 16, 302, 10456, 564842, 43545676, 4528889822, 610057244176, 103185102761042, 21388501828276756, 5328050642207280902, 1569616725144816645016, 539516138161105990193402

Offset

0,2

Links

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

Formula

a(n) = 2*Sum(k=1..2*n, Sum(t=0..n-k, binomial(2*n,2*t+k)*((Sum(j=k..2*n-2*t-k, binomial(j-1,k-1)*j!*Stirling2(2*n-2*t-k,j)*(-1)^(n+j)*2^(-2*t-k+2*n-j)))*Sum(i=0..k/2, (2*i-k)^(2*t+k)*binomial(k,i)*(-1)^(k-i))))/(2^k*k!)), n>0, a(0)=1. - Vladimir Kruchinin, Jun 30 2011

a(n) ~ (2*n)! * 2^(2*n-1/2) * exp(1/Pi + 4*sqrt(n/Pi)) / (n^(3/4) * Pi^(2*n+3/4)) * (1 - (5*Pi^2-2) / (12*Pi^(3/2)*sqrt(n))). - Vaclav Kotesovec, Jan 24 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[E^(Sin[x]*Tan[x]), {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 24 2015 *)

Prog

(Maxima)
a(n):=if n=0 then 1 else 2*sum(sum(binomial(2*n, 2*t+k)*((sum(binomial(j-1, k-1)*j!*stirling2(2*n-2*t-k, j)*(-1)^(n+j)*2^(-2*t-k+2*n-j), j, k, 2*n-2*t-k))*sum((2*i-k)^(2*t+k)*binomial(k, i)*(-1)^(k-i), i, 0, k/2)), t, 0, n-k)/(2^k*k!), k, 1, 2*n); /* Vladimir Kruchinin, Jun 30 2011 */

Crossrefs

Sequence in context: A259647 A188985 A362734 * A335618 A174487 A140051

Adjacent sequences: A009247 A009248 A009249 * A009251 A009252 A009253

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Status

approved