A009446 Expansion of 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, -165613871131289362192596992, 34644281516790333651724337152

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..300

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

Maple

S:= series(sin(x*cos(x)), x, 60):
seq(coeff(S, x, i)*i!, i=1..59, 2); # Robert Israel, Oct 09 2024

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