A168468 E.g.f. sec(log(1+tanh(x)))

1, 0, 1, -3, 8, -40, 256, -1568, 11108, -96720, 908836, -9084108, 101147408, -1233325600, 15998088016, -221845635248, 3301710539408, -52192183735680, 871157943761296, -15360373687021488, 285403775884452608

Offset

0,4

Links

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

Formula

a(n)=2*sum(m=1..n/2, (sum(j=0..m, binomial(2*j,j)*4^(m-2*j)*sum(i=0..j, (i-j)^(2*m)* binomial(2*j,i)*(-1)^(m+j-i))))*sum(r=2*m..n, (stirling1(r,2*m)*sum(k=r..n, binomial(k-1,r-1)*k!*2^(n-k)*stirling2(n,k)*(-1)^(r+k)))/r!)), n>0, a(0)=1.

Mathematica

With[{nn=20}, CoefficientList[Series[Sec[Log[1+Tanh[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 06 2011 *)

Prog

(Maxima)
a(n):=if n=0 then 1 else 2*sum((sum(binomial(2*j, j)*4^(m-2*j)*sum((i-j)^(2*m)*binomial(2*j, i)*(-1)^(m+j-i), i, 0, j), j, 0, m))*sum((stirling1(r, 2*m)*sum(binomial(k-1, r-1)*k!*2^(n-k)*stirling2(n, k)*(-1)^(r+k), k, r, n))/r!, r, 2*m, n), m, 1, n/2);

Crossrefs

Sequence in context: A107991 A007175 A152394 * A330527 A224246 A128322

Adjacent sequences: A168465 A168466 A168467 * A168469 A168470 A168471

Keyword

sign

Author

Vladimir Kruchinin, Jun 21 2011

Status

approved