OFFSET
0,3
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
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved