A009189 Expansion of e.g.f.: exp(cos(x)*x).

1, 1, 1, -2, -11, -24, 61, 624, 1737, -7424, -88679, -242560, 2086525, 23499776, 45950997, -1002251264, -9763133167, -2151563264, 705668046769, 5583112077312, -17356978593659, -666018502836224, -3823112141007763, 39230927775531008, 788728947108214489

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..560

Formula

a(n) = (sum(k=1..n-1, binomial(n,k)*(-1)^((n-k)/2)*(1+(-1)^(n-k))/(2^(k))*sum(i=0..floor((k-1)/2)), binomial(k,i)*(k-2*i)^(n-k)))+1. - Vladimir Kruchinin, Apr 21 2011

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * (2*k+1) * a(n-2*k-1). - Ilya Gutkovskiy, Mar 10 2022

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[Cos[x]*x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 15 2018 *)

Prog

(Maxima) a(n):=(sum(binomial(n, k)*(-1)^((n-k)/2)*(1+(-1)^(n-k))/(2^(k))*sum(binomial(k, i)*(k-2*i)^(n-k), i, 0, floor((k-1)/2)), k, 1, n-1))+1; /* Vladimir Kruchinin, Apr 21 2011 */
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x*cos(x)))) \\ Seiichi Manyama, Mar 26 2022

Crossrefs

Cf. A003727, A352252.

Sequence in context: A256905 A294547 A294557 * A370338 A012213 A012251

Adjacent sequences: A009186 A009187 A009188 * A009190 A009191 A009192

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Mar 15 2018

Status

approved