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 A371066 #11 Mar 10 2024 08:16:01
%S A371066 1,0,0,1,4,10,20,175,2296,20244,134520,1016565,13527580,209970046,
%T A371066 2785823404,33569936855,467250784560,8358652382760,159820481883696,
%U A371066 2888819281378089,51781860691882740,1031576680142770930,23237341150372569220,543570375735294712651
%N A371066 E.g.f. satisfies A(x) = 1 + x^3/6*exp(x*A(x)).
%F A371066 a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-3*k+1,k)/( 6^k*(n-3*k+1)*(n-3*k)! ).
%t A371066 nmax = 20; CoefficientList[Series[1 - ProductLog[-E^x*x^4/6]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Mar 10 2024 *)
%o A371066 (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-3*k+1, k)/(6^k*(n-3*k+1)*(n-3*k)!));
%Y A371066 Cf. A161631, A371063.
%Y A371066 Cf. A371044.
%K A371066 nonn
%O A371066 0,5
%A A371066 _Seiichi Manyama_, Mar 09 2024