A009015 Expansion of E.g.f.: cos(x*cos(x)) (even powers only).

1, -1, 13, -181, 3865, -140521, 6324517, -344747677, 23853473329, -1996865965009, 193406280000061, -21615227339380357, 2778071540350106953, -403985610499148666041, 65635628800688339178325

Offset

0,3

Links

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

Formula

a(n) = Sum_{j=0..(2*n-1)/2} binomial(2*n,2*j)*((Sum_{i=0..((2*j-1)/2)} (j-i)^(2*n-2*j)*binomial(2*j,i)))*(-1)^(n))/(2^(4*j-2*n-1)))+(-1)^n. - Vladimir Kruchinin, Jun 06 2011

Maple

seq(coeff(series(factorial(n)*(cos(x*cos(x))), x, n+1), x, n), n=0..30, 2); # Muniru A Asiru, Jul 21 2018

Mathematica

With[{nmax = 60}, CoefficientList[Series[Cos[x*Cos[x]], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]] (* G. C. Greubel, Jul 21 2018 *)

Prog

(Maxima)
a(n):=sum(binomial(2*n, 2*j)*((sum((j-i)^(2*n-2*j)*binomial(2*j, i), i, 0, ((2*j-1)/2)))*(-1)^(n))/(2^(4*j-2*n-1)), j, 0, (2*n-1)/2)+(-1)^n; /* Vladimir Kruchinin, Jun 06 2011 */
(PARI) x='x+O('x^50); v=Vec(serlaplace(cos(x*cos(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Jul 21 2018

Crossrefs

Sequence in context: A001570 A239902 A020544 * A067385 A097260 A178303

Adjacent sequences: A009012 A009013 A009014 * A009016 A009017 A009018

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved