A009596 Expansion of e.g.f. sinh(sin(x)^2) (even powers only).

0, 2, -8, 152, -6848, 312992, -17468288, 1385712512, -143250864128, 17321985331712, -2418583050119168, 396575082357512192, -75839817371814084608, 16517549362496506929152

Offset

0,2

Links

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

Formula

a(n) = 8*Sum_{j=1..n} 2^(2*n-4*j)/(2*j-1)!*Sum_{i=0..2*j-1} (i-2*j+1)^(2*n)*binomial(4*j-2,i)*(-1)^(n-1-i). - Vladimir Kruchinin, Jun 08 2011

Example

sinh(sin(x)*sin(x)) = 2/2!*x^2 - 8/4!*x^4 + 152/6!*x^6 - 6848/8!*x^8... - Patrick Demichel (patrick.demichel(AT)hp.com)

Mathematica

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

Prog

(Maxima)
a(n):=8*sum(2^(2*n-4*j)/(2*j-1)!*sum((i-2*j+1)^(2*n)*binomial(4*j-2, i)*(-1)^(n-1-i), i, 0, 2*j-1), j, 1, n); /* Vladimir Kruchinin, Jun 08 2011 */
(PARI) x='x+O('x^50); v=Vec(serlaplace(sinh(sin(x)^2))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Jan 30 2018

Crossrefs

Sequence in context: A007314 A102099 A012298 * A012571 A018926 A012432

Adjacent sequences: A009593 A009594 A009595 * A009597 A009598 A009599

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved