A339515 a(n) = Sum_{k=0..floor(n/3)} k! * (n - 3*k)!.

1, 1, 2, 7, 25, 122, 728, 5066, 40444, 363618, 3633894, 39957372, 479365980, 6230659848, 87218289408, 1308154099944, 20929024197336, 355774686465840, 6403682340295200, 121666035674658960, 2433257870201802720, 51097347163646718480, 1124122414761046131120

Offset: 0

Author

Vaclav Kotesovec, Dec 07 2020

Keywords

• nonn

Crossrefs

Cf. A096161, A309619.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}] * Sum[k!*x^(3*k), {k, 0, nmax}], {x, 0, nmax}], x]
Table[Sum[k!*(n - 3*k)!, {k, 0, Floor[n/3]}], {n, 0, 25}]

PARI

a(n) = sum(k=0, n\3, k! * (n - 3*k)!); \\ Michel Marcus, Dec 08 2020

Formula

G.f.: B(x)*B(x^3), where B(x) is g.f. of A000142.

a(n) ~ n! * (1 + 1/n^3 + 3/n^4 + 7/n^5 + 17/n^6 + 61/n^7 + 343/n^8 + 2233/n^9 + 14373/n^10 + ...).