A009801 - OEIS

%I #18 Apr 02 2017 12:26:58

%S 0,2,-8,-208,13312,-80128,-84819968,9993992192,759755210752,

%T -560066285928448,72155207745667072,37670722015948439552,

%U -22728912607776874692608,734502681629602026094592,6152371237231406870966566912,-3384992827698865393138954928128

%N E.g.f. tanh(sin(x)*sin(x)) (even powers only).

%F a(n)=2*sum(m=1..2*n, ((sum(k=1..m, (-1)^(k+1)*k!*2^(2*n-m-k)*stirling2(m,k)))*sum(i=0..m, (i-m)^(2*n)*binomial(2*m,i)*(-1)^(n+m-i)))/(m!)). - _Vladimir Kruchinin_, Jun 28 2011

%e tanh(sin(x)*sin(x)) = 2/2!*x^2-8/4!*x^4-208/6!*x^6+13312/8!*x^8...

%t With[{nn=30},Take[CoefficientList[Series[Tanh[Sin[x]^2],{x,0,nn}],x] Range[ 0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Apr 07 2014 *)

%o (Maxima)

%o a(n):=2*sum(((sum((-1)^(k+1)*k!*2^(2*n-m-k)*stirling2(m,k),k,1,m))*sum((i-m)^(2*n)*binomial(2*m,i)*(-1)^(n+m-i),i,0,m))/(m!),m,1,2*n); /* _Vladimir Kruchinin_, Jun 28 2011 */

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E More terms from _Harvey P. Dale_, Apr 07 2014