A009377 E.g.f. log(1 + tan(x)*sin(x)) (even powers only).

0, 2, -8, 182, -6008, 408122, -38757908, 5438711462, -1008011932208, 244100206825202, -74027819501268908, 27620824218436349342, -12405602584546021488008, 6609444480661620416243882

Offset

0,2

Links

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

Formula

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

a(n) ~ (2*n)! * (-1)^(n+1) / (n * (log((1 + sqrt(5) + sqrt(2*(1 + sqrt(5)))) / 2))^(2*n)). - Vaclav Kotesovec, Jan 24 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Log[1 + 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):=sum(((-1)*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+2*n-2*k-j+1), j, k, 2*n-2*t-k))*sum((2*i-k)^(2*t+k)*binomial(k, i)*(-1)^(i), i, 0, k/2)), t, 0, n-k))/(k), k, 1, 2*n); /* Vladimir Kruchinin, Jun 30 2011 */

Crossrefs

Sequence in context: A265597 A213200 A317794 * A181234 A156526 A009505

Adjacent sequences: A009374 A009375 A009376 * A009378 A009379 A009380

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved