A352250 Expansion of e.g.f. 1 / (1 - x * sin(x)) (even powers only).

1, 2, 20, 486, 21944, 1591210, 169207092, 24808395262, 4796420822384, 1182349445882706, 361939981107422060, 134705596642758848806, 59900689507397744253096, 31365504832631796986962426, 19102102945852191813235300004, 13387748268024668296590660222030

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1; a(n) = 2 * Sum_{k=1..n} (-1)^(k+1) * binomial(2*n,2*k) * k * a(n-k).

Mathematica

nmax = 30; Take[CoefficientList[Series[1/(1 - x Sin[x]), {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]
a[0] = 1; a[n_] := a[n] = 2 Sum[(-1)^(k + 1) Binomial[2 n, 2 k] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]

Prog

(PARI) my(x='x+O('x^40), v=Vec(serlaplace(1 /(1-x*sin(x))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Mar 10 2022

Crossrefs

Cf. A000111, A000364, A009214, A205571, A210657, A302397, A352251, A352252.

Sequence in context: A274572 A292396 A274738 * A012816 A012340 A279839

Adjacent sequences: A352247 A352248 A352249 * A352251 A352252 A352253

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 09 2022

Status

approved