A009518 Expansion of e.g.f. sin(tan(x)^2) (even powers only).

0, 2, 16, 152, -5504, -1107808, -155757824, -22741022848, -3557729644544, -565165935635968, -73212906789515264, 4150737348343519232, 11583034460298696687616, 8797240254608561943191552

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Examples

			sin(tan(x)*tan(x))=2/2!*x^2+16/4!*x^4+152/6!*x^6-5504/8!*x^8...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Programs

Mathematica

With[{nn=30},Take[CoefficientList[Series[Sin[Tan[x]^2],{x,0,nn}], x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, May 17 2012 *)

Maxima

a(n):=sum(sum(binomial(j-1,4*m+1)*(j)!*2^(2*n-j)*(-1)^(n+m+j+1)*stirling2(2*n,j),j,4*m+2,2*n)/(2*m+1)!,m,0,(n-1)/2); /* Vladimir Kruchinin, Jun 10 2011 */

Formula

a(n) = sum(m=0..(n-1)/2, sum(j=4*m+2..2*n, binomial(j-1,4*m+1)*(j)!*2^(2*n-j)*(-1)^(n+m+j+1)*stirling2(2*n,j))/(2*m+1)!). - Vladimir Kruchinin, Jun 10 2011

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997