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

Author

R. H. Hardin

Keywords

• sign

Links

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

Programs

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 *)

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 */

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997