A009249 E.g.f. exp(tan(x)*log(1+x)).

1, 0, 2, -3, 28, -110, 1010, -6636, 67856, -618120, 7231048, -82977400, 1111357256, -15222508080, 231587495568, -3664098311160, 62674059676416, -1120961847782976, 21339716663592384, -424956180060612864

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n)=sum(k=1..n, sum(i=0..n/2-k, binomial(n,2*i+k)*((sum(j=0..2*i, stirling2(2*i+k,j+k)*2^(-j+2*i-1)*binomial(j+k-1,k-1)*(j+k)!*(-1)^(i+j)))*stirling1(n-2*i-k,k)))), n>0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011

a(n) ~ n! * (-1)^n * n^(tan(1)-1) / GAMMA(tan(1)). - Vaclav Kotesovec, Jan 24 2015

Mathematica

Exp[ Tan[ x ]*Log[ 1+x ] ]
CoefficientList[Series[(1 + x)^Tan[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

Prog

(Maxima)
a(n):=sum(sum(binomial(n, 2*i+k)*((sum(stirling2(2*i+k, j+k)*2^(-j+2*i-1)*binomial(j+k-1, k-1)*(j+k)!*(-1)^(i+j), j, 0, 2*i))*stirling1(n-2*i-k, k)), i, 0, n/2-k), k, 1, n); /* Vladimir Kruchinin, Jun 01 2011 */

Crossrefs

Sequence in context: A279600 A280140 A037423 * A012697 A191470 A001094

Adjacent sequences: A009246 A009247 A009248 * A009250 A009251 A009252

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved