A292889 - OEIS

%I #34 Jul 10 2022 09:41:24

%S 1,0,0,6,24,60,480,5250,40656,302904,3024720,35260830,400499880,

%T 4619610996,58758862344,813678468330,11686918766880,173172973038960,

%U 2695921067029536,44219170187746614,755363769931590840,13351503268881437100,244634794020399856920

%N Expansion of e.g.f. exp(x^3 * exp(x)).

%H Seiichi Manyama, <a href="/A292889/b292889.txt">Table of n, a(n) for n = 0..498</a>

%F a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k)/(k! * (n-3*k)!). - _Seiichi Manyama_, Jul 10 2022

%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(x^3*exp(x))))

%o (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)/(k!*(n-3*k)!)); \\ _Seiichi Manyama_, Jul 10 2022

%Y Column k=3 of A292978.

%Y Cf. A145453, A292891, A292908.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 26 2017