A009546 Expansion of e.g.f. sin(x)*sin(sin(x)) (even powers only).

0, 2, -12, 118, -1816, 37354, -974372, 31769182, -1259350576, 59073098706, -3226127944764, 202778723085382, -14503292667068744, 1168138817072817594, -105070093531389641300, 10481640556778901446190, -1152522131016352310551648

Offset

0,2

Links

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

Formula

a(n) = 2*Sum_{k=1..n} (4^(n-k)*Sum_{i=0..k} (i-k)^(2*n)*binomial(2*k,i)*(-1)^(n-i-1))/(2*k-1)!). - Vladimir Kruchinin, Jun 28 2011

Mathematica

With[{nmax = 50}, CoefficientList[Series[Sin[x]*Sin[Sin[x]], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; ;; 2]] (* G. C. Greubel, Jan 20 2018 *)

Prog

(Maxima)
a(n):=2*sum((4^(n-k)*sum((i-k)^(2*n)*binomial(2*k, i)*(-1)^(n-i-1), i, 0, k))/(2*k-1)!, k, 1, n); /* Vladimir Kruchinin, Jun 28 2011 */
(PARI) x='x+O('x^50); v=Vec(serlaplace(sin(x)*sin(sin(x)))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Jan 20 2018

Crossrefs

Sequence in context: A279201 A121425 A132692 * A009748 A212414 A305051

Adjacent sequences: A009543 A009544 A009545 * A009547 A009548 A009549

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved