OFFSET
0,4
FORMULA
a(n)=sum(m=0..(n-1)/2, (sum(j=1..2*m+1, j!*2^(2*m-j+1)*(-1)^(m+j+1)* stirling2(2*m+1,j)))*sum(r=2*m+1..n,(stirling1(r,2*m+1)*sum(k=r..n, binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k)))/r!)). - Vladimir Kruchinin, Jun 21 2011
a(n) ~ (-1)^(n+1) * n! / ((2-exp(-Pi/2)) * (log(2*exp(Pi/2)-1)/2)^(n+1)). - Vaclav Kotesovec, Feb 02 2015
MATHEMATICA
CoefficientList[Series[Tan[Log[1+Tanh[x]]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 02 2015 *)
PROG
(Maxima)
a(n):=sum((sum(j!*2^(2*m-j+1)*(-1)^(m+j+1)*stirling2(2*m+1, j), j, 1, 2*m+1))*sum((stirling1(r, 2*m+1)*sum(binomial(k-1, r-1)*k!*2^(n-k)*stirling2(n, k)*(-1)^(r+k), k, r, n))/r!, r, 2*m+1, n), m, 0, (n-1)/2); /* Vladimir Kruchinin Jun 21 2011 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified by Harvey P. Dale, Jun 20 2023
STATUS
approved