A009613 Expansion of e.g.f. sinh(tan(x)*tan(x)) (even powers only).

0, 2, 16, 392, 21376, 1875872, 227105536, 35750690432, 7110343684096, 1750588208886272, 523940264885702656, 187423773435078920192, 78905518064423548911616, 38568578386644134655598592

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Examples

			sinh(tan(x)*tan(x)) = 2/2!*x^2 + 16/4!*x^4 + 392/6!*x^6 + 21376/8!*x^8 + ...
		

Programs

Mathematica

With[{nn=30},Take[CoefficientList[Series[Sinh[Tan[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Jun 12 2016 *)

Maxima

a(n):=sum(1/(2*m+1)!*sum(binomial(j-1,4*m+1)*j!*2^(2*n-j)*(-1)^(n+1+j)*stirling2(2*n,j),j,4*m+2,2*n),m,0,n); /* Vladimir Kruchinin, Jun 11 2011 */

Formula

a(n) = sum(m=0..n, 1/(2*m+1)!*sum(j=4*m+2..2*n, binomial(j-1,4*m+1)*j!*2^(2*n-j)*(-1)^(n+1+j)*stirling2(2*n,j))). - Vladimir Kruchinin, Jun 11 2011

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997