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 A317103 #16 Feb 16 2025 08:33:56
%S A317103 0,1,4,27,220,2265,27246,393421,6548536,126257697,2767122010,
%T A317103 68387691141,1882488882660,57198150690577,1900138953826582,
%U A317103 68502961685976525,2662089147552365296,110887849449189768513,4926985461324765096498,232544882903837769171829
%N A317103 Expansion of e.g.f. -LambertW(-x) * Product_{k>=1} 1/(1-x^k).
%H A317103 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>
%H A317103 Wikipedia, <a href="http://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>
%F A317103 a(n) ~ c * n^(n-1), where c = 1/QPochhammer(exp(-1)) = 1.98244090741287370368568246556131... - _Vaclav Kotesovec_, Jul 21 2018
%t A317103 nmax = 20; CoefficientList[Series[-LambertW[-x]*Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
%t A317103 Table[n!*Sum[PartitionsP[n-k]*k^(k-1)/k!, {k, 1, n}], {n, 0, 20}]
%Y A317103 Cf. A000041, A000169, A252761, A291332, A291333, A317104.
%K A317103 nonn
%O A317103 0,3
%A A317103 _Vaclav Kotesovec_, Jul 21 2018