A191995 E.g.f. arctan(log(1+tanh(x))).

0, 1, -1, -2, 14, -6, -406, 2220, 13768, -280224, 501824, 34875600, -394160416, -3296452368, 129418793776, -532969950240, -35512135858048, 654965382945408, 5943454902108032, -395494767434053632, 2913398252129581312

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n)=sum(m=0..(n-1)/2, ((-1)^(m)*(2*m+1)!*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!))/(2*m+1)), n>0.

Mathematica

With[{nn=30}, CoefficientList[Series[ArcTan[Log[1+Tanh[x]]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jan 03 2013 *)

Prog

(Maxima)
a(n):=sum(((-1)^(m)*(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))/(2*m+1), m, 0, (n-1)/2);

Crossrefs

Sequence in context: A084677 A344115 A373790 * A168207 A082609 A271382

Adjacent sequences: A191992 A191993 A191994 * A191996 A191997 A191998

Keyword

sign

Author

Vladimir Kruchinin, Jun 21 2011

Status

approved