A370699 Expansion of e.g.f. exp(-x^3/6)/(1-x).

1, 1, 2, 5, 20, 100, 610, 4270, 34160, 307160, 3071600, 33787600, 405466600, 5271065800, 73794921200, 1106922416600, 17710758665600, 301082897315200, 5419492342264000, 102970354503016000, 2059407090060320000, 43247548855054544000, 951446074811199968000

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k/(6^k * k!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3/6)/(1-x)))
(PARI) a(n) = n!*sum(k=0, n\3, (-1)^k/(6^k*k!));

Crossrefs

Cf. A000166, A000266.

Sequence in context: A074415 A020001 A348597 * A039909 A009551 A323274

Adjacent sequences: A370696 A370697 A370698 * A370700 A370701 A370702

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 27 2024

Status

approved