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 A354136 #9 May 18 2022 13:12:51
%S A354136 1,0,0,1,-6,35,-215,1414,-9912,73044,-552570,4102626,-26654826,
%T A354136 79506492,2154425364,-73527421176,1708053626880,-35961691589640,
%U A354136 736338276883080,-15067241745943680,312009998091705720,-6579362641255341120,141704946709227843480
%N A354136 Expansion of e.g.f. exp(log(1 + x)^3/6).
%F A354136 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * Stirling1(k,3) * a(n-k).
%F A354136 a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling1(n,3*k)/(6^k * k!).
%o A354136 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1+x)^3/6)))
%o A354136 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, binomial(i-1, j-1)*stirling(j, 3, 1)*v[i-j+1])); v;
%o A354136 (PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 1)/(6^k*k!));
%Y A354136 Cf. A354137.
%Y A354136 Cf. A327504, A347002, A354134.
%K A354136 sign
%O A354136 0,5
%A A354136 _Seiichi Manyama_, May 18 2022