A009057 Expansion of e.g.f. x*cos(sinh(x)) (odd powers only).

1, -3, -15, 21, 1953, 32461, 77649, -18557595, -894805183, -21405607651, 421226202033, 90171090228021, 6418365899545825, 230309031988304109, -11126456208720437487, -3093396343171182148731, -342554566975833968005503

Offset

0,2

Links

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

Formula

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

Mathematica

With[{nn=40}, Take[CoefficientList[Series[x Cos[Sinh[x]], {x, 0, nn}], x] Range[ 0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, May 22 2017 *)

Prog

(Maxima)
a(n):=if n=0 then 1 else (sum((sum((-1)^(i+m/2)*(m-2*i)^(2*n)*binomial(m, i), i, 0, m))/(2^m*m!), m, 1, 2*n))*(2*n+1); /* Vladimir Kruchinin, Jun 28 2011 */
(PARI) x='x+O('x^60); v=Vec(serlaplace(x*cos(sinh(x)))); vector((#v-1)\2 , n, v[2*n-1]) \\ G. C. Greubel, Jul 23 2018

Crossrefs

Sequence in context: A087674 A212846 A276804 * A289712 A083795 A083793

Adjacent sequences: A009054 A009055 A009056 * A009058 A009059 A009060

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved