A375628 - OEIS

%I #9 Aug 22 2024 09:17:14

%S 1,1,2,18,96,600,5760,57960,645120,8285760,117936000,1842825600,

%T 31374604800,578334556800,11493004723200,244720360684800,

%U 5555523785011200,134002274473267200,3422904611167641600,92290617116425728000,2619214995575033856000

%N Expansion of e.g.f. exp(2*x^3) / (1 - x * exp(x^3)).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+2)^k/k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^3)/(1-x*exp(x^3))))

%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k+2)^k/k!);

%Y Cf. A368265, A375627.

%Y Cf. A358065, A375607.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 21 2024