A351880 Expansion of e.g.f. 1 / (1 - x)^cos(x).

1, 1, 2, 3, 6, 15, 105, 924, 8204, 73461, 700005, 7323976, 84472146, 1064285027, 14492861747, 211738655608, 3302847261448, 54800458320345, 963864555797385, 17914985159719376, 350861004976886190, 7221748369472388727, 155853930324297011719, 3519121773604369318856

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} (-1)^k * binomial(n-1,k-1) * A009410(k) * a(n-k).

a(n) ~ n! * n^(cos(1)-1) / Gamma(cos(1)). - Vaclav Kotesovec, Feb 23 2022

Mathematica

nmax = 23; CoefficientList[Series[1/(1 - x)^Cos[x], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^cos(x))) \\ Michel Marcus, Feb 23 2022

Crossrefs

Cf. A007118, A007119, A009192, A009410, A298374, A351881.

Sequence in context: A305857 A014627 A145781 * A109162 A215659 A028688

Adjacent sequences: A351877 A351878 A351879 * A351881 A351882 A351883

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2022

Status

approved