A009801 E.g.f. tanh(sin(x)*sin(x)) (even powers only).

0, 2, -8, -208, 13312, -80128, -84819968, 9993992192, 759755210752, -560066285928448, 72155207745667072, 37670722015948439552, -22728912607776874692608, 734502681629602026094592, 6152371237231406870966566912, -3384992827698865393138954928128

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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

Example

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

Mathematica

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 *)

Prog

(Maxima)
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 */

Crossrefs

Sequence in context: A012539 A012535 A012300 * A012297 A000893 A030177

Adjacent sequences: A009798 A009799 A009800 * A009802 A009803 A009804

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

More terms from Harvey P. Dale, Apr 07 2014

Status

approved