A009048 Expansion of e.g.f. cos(sin(x)*exp(x)).

1, 0, -1, -6, -19, -20, 203, 1862, 9305, 20472, -159849, -2441230, -17558715, -60043100, 365766243, 8445023358, 80287239857, 383311153776, -1756145007825, -61596647223446, -735340088843107, -4522824431862308, 15016682566162427

Offset

0,4

Links

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

Formula

a(n) = Sum_{k=1..n/2} 2^(n-2*k+1)*Sum_{j=k..n/2} binomial(n,n-2*j)*((k)^(n-2*j)*Sum_{i=0..k} (i-k)^(2*j)*binomial(2*k,i)*(-1)^(j-i)))/(2*k)!. - Vladimir Kruchinin, Jun 13 2011

Maple

seq(coeff(series(factorial(n)*cos(sin(x)*exp(x)), x, n+1), x, n), n=0..25); # Muniru A Asiru, Jul 24 2018

Mathematica

With[{nn=30}, CoefficientList[Series[Cos[Sin[x]Exp[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 10 2015 *)

Prog

(Maxima)
a(n):=sum((2^(n-2*k+1)*sum(binomial(n, n-2*j)*((k)^(n-2*j)*sum((i-k)^(2*j)*binomial(2*k, i)*(-1)^(j-i), i, 0, k)), j, k, n/2))/(2*k)!, k, 1, n/2); /* Vladimir Kruchinin, Jun 13 2011 */
(PARI) x='x+O('x^30); Vec(serlaplace(cos(sin(x)*exp(x)))) \\ G. C. Greubel, Jul 23 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Sin(x)*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 23 2018

Crossrefs

Sequence in context: A184197 A173568 A012589 * A294313 A235537 A046955

Adjacent sequences: A009045 A009046 A009047 * A009049 A009050 A009051

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved