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 A330649 #82 Feb 16 2020 05:45:01
%S A330649 1,1,5,34,299,3226,41202,607545,10153831,189628750,3913009178,
%T A330649 88406043991,2170372901534,57531498837515,1637713270797411,
%U A330649 49830222530823615,1613950394999111903,55444724259894089718,2013760368429942861810,77105255895256112519259
%N A330649 E.g.f.: Product_{k>=1} 1 / (1 - x^k/(k!*(1 - x)^k)).
%F A330649 a(n) = Sum_{k=0..n} binomial(n-1,k-1) * A005651(k) * n! / k!.
%F A330649 a(n) ~ c * 2^(n-1) * n!, where c = A247551 = 2.52947747207915264818... - _Vaclav Kotesovec_, Feb 16 2020
%t A330649 nmax = 19; CoefficientList[Series[Product[1/(1 - x^k/(k! (1 - x)^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A330649 Table[Sum[Binomial[n - 1, k - 1] Total[Apply[Multinomial, IntegerPartitions[k], {1}]] n!/k!, {k, 0, n}], {n, 0, 19}]
%o A330649 (PARI) seq(n)={Vec(serlaplace(prod(k=1, n, 1 / (1 - x^k/(k!*(1 - x)^k)) + O(x*x^n))))} \\ _Andrew Howroyd_, Feb 13 2020
%Y A330649 Cf. A005651, A084358, A218482, A320566, A332024.
%K A330649 nonn
%O A330649 0,3
%A A330649 _Ilya Gutkovskiy_, Feb 13 2020