A009640 Expansion of e.g.f.: tan(log(1+tanh(x))).

0, 1, -1, 2, -10, 46, -226, 1532, -11880, 96136, -882376, 9179312, -102310000, 1223945776, -15941391376, 222827194592, -3303846357120, 52077034777216, -871329939918976, 15375474411183872, -285315305595562240, 5562663216718387456, -113653337185088018176

Offset

0,4

Links

Table of n, a(n) for n=0..22.

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

Sequence in context: A137635 A029706 A191644 * A191684 A081167 A321274

Adjacent sequences: A009637 A009638 A009639 * A009641 A009642 A009643

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified by Harvey P. Dale, Jun 20 2023

Status

approved