A009446 E.g.f. sin(x*cos(x)) (odd powers only)

1, -4, 36, -848, 23824, -871872, 44942912, -2860930816, 213856723200, -19099352929280, 2010469524579328, -242177953175506944, 32998102512641970176, -5069553933584348397568, 870871673923373487243264

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

a(n)=(-1)^(n)*sum(k=0..n, binomial(2*n+1,2*k+1)*((sum(i=0..k, (2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i))))/(2^(2*k))). - Vladimir Kruchinin, Jun 18 2011

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sin[x Cos[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Oct 04 2017 *)

Prog

(Maxima)
a(n):=(-1)^(n)*sum(binomial(2*n+1, 2*k+1)*((sum((2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1, i), i, 0, ((k)))))/(2^(2*k)), k, 0, n); /* Vladimir Kruchinin, Jun 18 2011 */

Crossrefs

Sequence in context: A214669 A126152 A353996 * A134052 A127901 A061742

Adjacent sequences: A009443 A009444 A009445 * A009447 A009448 A009449

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved