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 A357192 #10 Sep 17 2022 08:50:09
%S A357192 1,0,0,6,24,120,23760,327600,5201280,1283688000,37574409600,
%T A357192 1219438281600,378254710310400,19092171351052800,1045282110435763200,
%U A357192 394211859168070944000,30499777423295212032000,2523689643597315088896000,1125362204955051396299366400
%N A357192 a(n) = n! * Sum_{k=0..floor(n/3)} k^n/k!.
%F A357192 E.g.f.: Sum_{k>=0} (k * x)^(3 * k) / (k! * (1 - k * x)).
%o A357192 (PARI) a(n) = n!*sum(k=0, n\3, k^n/k!);
%o A357192 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^(3*k)/(k!*(1-k*x)))))
%Y A357192 Cf. A256016, A357191.
%Y A357192 Cf. A352982, A357194.
%K A357192 nonn
%O A357192 0,4
%A A357192 _Seiichi Manyama_, Sep 17 2022