|
%I #9 Dec 08 2020 06:43:40
%S 1,1,2,7,25,122,728,5066,40444,363618,3633894,39957372,479365980,
%T 6230659848,87218289408,1308154099944,20929024197336,355774686465840,
%U 6403682340295200,121666035674658960,2433257870201802720,51097347163646718480,1124122414761046131120
%N a(n) = Sum_{k=0..floor(n/3)} k! * (n - 3*k)!.
%F G.f.: B(x)*B(x^3), where B(x) is g.f. of A000142.
%F 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 + ...).
%t nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}] * Sum[k!*x^(3*k), {k, 0, nmax}], {x, 0, nmax}], x]
%t Table[Sum[k!*(n - 3*k)!, {k, 0, Floor[n/3]}], {n, 0, 25}]
%o (PARI) a(n) = sum(k=0, n\3, k! * (n - 3*k)!); \\ _Michel Marcus_, Dec 08 2020
%Y Cf. A096161, A309619.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Dec 07 2020
|
