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 A357194 #12 Sep 17 2022 08:48:43 %S A357194 1,0,0,6,24,120,94372560,5284828080,338228714880,461220488356944960, %T A357194 124524904888012809600,36983489578531184304000, %U A357194 94262861823240343196388902400,78420937396722501660156363686400,70262981254649802508019882162611200 %N A357194 a(n) = n! * Sum_{k=0..floor(n/3)} k^(3*n)/k!. %F A357194 E.g.f.: Sum_{k>=0} (k^3 * x)^(3 * k) / (k! * (1 - k^3 * x)). %o A357194 (PARI) a(n) = n!*sum(k=0, n\3, k^(3*n)/k!); %o A357194 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*x)^(3*k)/(k!*(1-k^3*x))))) %Y A357194 Cf. A256016, A357193. %Y A357194 Cf. A352984, A357192. %K A357194 nonn %O A357194 0,4 %A A357194 _Seiichi Manyama_, Sep 17 2022