A009591 Expansion of e.g.f. sinh(sin(x)) * sin(x) (even powers only).

0, 2, -4, -42, 888, -8086, -115468, 8863806, -275344656, 2488177106, 369676840940, -34139482063962, 1691837365047912, -16526563632072646, -7669129653528552220, 1088114395890103645710, -87525176659638470236704

Offset

0,2

Links

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

Formula

a(n) = 2*Sum_{j=1..n} 4^(n-j)/(2*j-1)!*Sum_{i=0..j-1} (i-j)^(2*n)* binomial(2*j,i)*(-1)^(n+j-i). - Vladimir Kruchinin, Jun 09 2011

Mathematica

With[{nn=40}, Take[CoefficientList[Series[Sinh[Sin[x]]Sin[x], {x, 0, nn}], x]Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Dec 08 2012 *)

Prog

(Maxima)
a(n):=2*sum(4^(n-j)/(2*j-1)!*sum((i-j)^(2*n)*binomial(2*j, i)*(-1)^(n+j-i), i, 0, j-1), j, 1, n); /* Vladimir Kruchinin, Jun 09 2011 */
(PARI) x='x+O('x^40); v=Vec(serlaplace(sinh(sin(x))*sin(x))); concat([0], vector(#v\2 , n, v[2*n-1])) \\ G. C. Greubel, Jan 30 2018

Crossrefs

Sequence in context: A215921 A009811 A364237 * A009717 A018317 A359876

Adjacent sequences: A009588 A009589 A009590 * A009592 A009593 A009594

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved