This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348312 #11 Oct 21 2021 01:25:34
%S A348312 0,1,8,51,312,1965,13248,97839,800208,7260921,72806040,801515979,
%T A348312 9620317512,125071036389,1751016829968,26265324194055,420245416687392,
%U A348312 7144172815479921,128595113003161512,2443307154421058019,48866143111666389720,1026189005418216656541,22576158119430894214368
%N A348312 a(n) = n! * Sum_{k=0..n-1} 3^k / k!.
%F A348312 E.g.f.: x * exp(3*x) / (1 - x).
%F A348312 a(0) = 0; a(n) = n * (a(n-1) + 3^(n-1)).
%F A348312 a(n) ~ exp(3)*n!. - _Stefano Spezia_, Oct 11 2021
%t A348312 Table[n! Sum[3^k/k!, {k, 0, n - 1}], {n, 0, 22}]
%t A348312 nmax = 22; CoefficientList[Series[x Exp[3 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%o A348312 (PARI) a(n) = n!*sum(k=0, n-1, 3^k/k!); \\ _Michel Marcus_, Oct 11 2021
%Y A348312 Cf. A007526, A053486, A066534, A348314.
%K A348312 nonn
%O A348312 0,3
%A A348312 _Ilya Gutkovskiy_, Oct 11 2021