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 A353884 #12 May 09 2022 15:19:40 %S A353884 1,0,0,0,0,0,20,210,1400,7560,36120,159390,1035100,17082780,329893564, %T A353884 5336661330,73265956400,889068944400,9968073461616,112902000191334, %U A353884 1531070090032500,27610559023112100,586336131631313140,12550716321612658266,254052845940651258600 %N A353884 Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^3 / 36). %F A353884 a(n) = n! * Sum_{k=0..floor(n/6)} (3*k)! * Stirling2(n-3*k,3*k)/(36^k * (n-3*k)!). %o A353884 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*(exp(x)-1))^3/36))) %o A353884 (PARI) a(n) = n!*sum(k=0, n\6, (3*k)!*stirling(n-3*k, 3*k, 2)/(36^k*(n-3*k)!)); %Y A353884 Cf. A052848, A353883, A353885. %Y A353884 Cf. A346894, A353881. %K A353884 nonn %O A353884 0,7 %A A353884 _Seiichi Manyama_, May 09 2022