A009595 Expansion of e.g.f. sinh(sin(x)*x), even powers only.

0, 2, -4, 126, -3368, 95770, -4408812, 265489238, -18154718416, 1485105153714, -146642787086420, 16695614806747822, -2147275569222109944, 312504772665433249226, -51165984479663630172988, 9306072483765112492581510

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

a(n) = Sum_{k=0..n-1} binomial(2*n,2*k+1)*(2^(-2*k)*Sum_{i=0..k} (2*i -2*k-1)^(2*n-2*k-1)*binomial(2*k+1,i)*(-1)^(n-i)). - Vladimir Kruchinin, Jun 29 2011

Mathematica

With[{nmax = 50}, CoefficientList[Series[Sinh[Sin[x]*x], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; ;; 2]] (* G. C. Greubel, Jan 30 2018 *)

Prog

(Maxima)
a(n):=sum(binomial(2*n, 2*k+1)*(2^(-2*k)*sum((2*i-2*k-1)^(2*n-2*k-1)*binomial(2*k+1, i)*(-1)^(n-i), i, 0, k)), k, 0, n-1); /* Vladimir Kruchinin, Jun 29 2011 */
(PARI) my(x='x+O('x^50)); v=Vec(serlaplace(sinh(x*sin(x)))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Jan 30 2018

Crossrefs

Sequence in context: A326204 A259381 A333621 * A018493 A046035 A376315

Adjacent sequences: A009592 A009593 A009594 * A009596 A009597 A009598

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved