A191463 E.g.f. (even powers only) cos(x)^(cos(x)-1)

1, 0, 6, 15, 1596, 28155, 2752266, 152499165, 18328556616, 2081907926295, 342948671262246, 63036450590713545, 14410958655520684956, 3796531150529363706915, 1173277778862573074248746, 415134737359852340707539405, 167697531024902643857808300816, 76517905142019788108453415876015

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Mathematica

With[{nn=40}, Take[CoefficientList[Series[Cos[x]^(Cos[x]-1), {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Mar 19 2018 *)

Prog

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

Crossrefs

Sequence in context: A307812 A354682 A280964 * A235943 A225304 A299709

Adjacent sequences: A191460 A191461 A191462 * A191464 A191465 A191466

Keyword

nonn

Author

Vladimir Kruchinin, Jun 03 2011

Status

approved