A009311 E.g.f. log(1+log(1+tanh(x))).

0, 1, -2, 5, -19, 104, -706, 5662, -53082, 570600, -6897016, 92565296, -1366706848, 22016867248, -384226243584, 7220865546000, -145397565641296, 3122890640031488, -71266398589322368, 1722010388581604224

Offset

0,3

Links

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

Formula

a(n)=sum(m=1..n, ((-1)^(m-1)*m!*sum(r=m..n, (stirling1(r,m)*sum(k=r..n, binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k)))/r!))/m). - Vladimir Kruchinin, Jun 21 2011

a(n) ~ (n-1)! * (-1)^(n+1) * 2^n / (log(2*exp(1)-1))^n. - Vaclav Kotesovec, Jan 22 2015

Mathematica

CoefficientList[Series[Log[1 + Log[1 + Tanh[x]]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)

Prog

(Maxima)
a(n):=sum(((-1)^(m-1)*m!*sum((stirling1(r, m)*sum(binomial(k-1, r-1)*k!*2^(n-k)*stirling2(n, k)*(-1)^(r+k), k, r, n))/r!, r, m, n))/m, m, 1, n); /* Vladimir Kruchinin, Jun 21 2011 */

Crossrefs

Sequence in context: A054687 A076669 A093502 * A211207 A107882 A328977

Adjacent sequences: A009308 A009309 A009310 * A009312 A009313 A009314

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved