A009249 - OEIS

%I #17 Apr 01 2017 13:26:23

%S 1,0,2,-3,28,-110,1010,-6636,67856,-618120,7231048,-82977400,

%T 1111357256,-15222508080,231587495568,-3664098311160,62674059676416,

%U -1120961847782976,21339716663592384,-424956180060612864

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

%F 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

%F a(n) ~ n! * (-1)^n * n^(tan(1)-1) / GAMMA(tan(1)). - _Vaclav Kotesovec_, Jan 24 2015

%t Exp[ Tan[ x ]*Log[ 1+x ] ]

%t CoefficientList[Series[(1 + x)^Tan[x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)

%o (Maxima)

%o 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 */

%K sign,easy

%O 0,3

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997