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 A318580 #7 Jan 09 2019 09:18:20
%S A318580 1,1,7,55,601,7561,116191,1999327,39267985,850964401,20332107991,
%T A318580 527930427751,14838001344937,447653776595065,14440021169407471,
%U A318580 495398956418435791,18012260306904120481,691502230924473978337,27948692251661337581095,1185878351946613955122711
%N A318580 Expansion of e.g.f. exp(-1 + Product_{k>=1} 1/(1 - x^k)^k).
%F A318580 E.g.f.: exp(-1 + exp(Sum_{k>=1} sigma_2(k)*x^k/k)).
%F A318580 E.g.f.: A(x) = exp(B(x) - 1), where B(x) = o.g.f. of A000219.
%F A318580 a(0) = 1; a(n) = Sum_{k=1..n} A000219(k)*k!*binomial(n-1,k-1)*a(n-k).
%p A318580 seq(n!*coeff(series(exp(-1+mul(1/(1-x^k)^k,k=1..100)),x=0,20),x,n),n=0..19); # _Paolo P. Lava_, Jan 09 2019
%t A318580 nmax = 19; CoefficientList[Series[Exp[-1 + Product[1/(1 - x^k)^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A318580 nmax = 19; CoefficientList[Series[Exp[-1 + Exp[Sum[DivisorSigma[2, k] x^k/k, {k, 1, nmax}]]], {x, 0, nmax}], x] Range[0, nmax]!
%t A318580 p[n_] := p[n] = Sum[DivisorSigma[2, k] p[n - k], {k, n}]/n; p[0] = 1; a[n_] := a[n] = Sum[p[k] k! Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]
%Y A318580 Cf. A000219, A001157, A058892, A318250.
%K A318580 nonn
%O A318580 0,3
%A A318580 _Ilya Gutkovskiy_, Aug 29 2018