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 A322612 #13 Jan 07 2019 03:34:20
%S A322612 1,0,2,9,68,490,5184,53928,696352,9545184,147901680,2437886880,
%T A322612 44593856064,861936989472,17988878376000,398199273907680,
%U A322612 9386173867046400,233068382185213440,6117261434418069504,168414066137504272896,4867992707164288773120,147081824197157871866880,4641822165217412602183680
%N A322612 Expansion of e.g.f. Product_{k>=1} 1/(1 + log(1 - x)*x^k).
%H A322612 Robert Israel, <a href="/A322612/b322612.txt">Table of n, a(n) for n = 0..427</a>
%F A322612 E.g.f.: exp(Sum_{k>=1} ( Sum_{d|k} log(1/(1 - x))^d/d ) * x^k).
%F A322612 a(n) ~ c * n! / r^n, where r = 0.74075364335169502373416717320773551326074821766... is the root of the equation r*log(1-r) = -1 and c = 1 / (r*(r/(1-r) - log(1-r)) * Product_{k>=2} (1 + log(1-r)*r^k) ) = 16.634865259935976898139371781860039862... - _Vaclav Kotesovec_, Dec 20 2018
%p A322612 seq(coeff(series(factorial(n)*mul((1+log(1-x)*x^k)^(-1),k=1..n),x,n+1), x, n), n = 0 .. 22); # _Muniru A Asiru_, Dec 21 2018
%t A322612 nmax = 22; CoefficientList[Series[Product[1/(1 + Log[1 - x] x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A322612 nmax = 22; CoefficientList[Series[Exp[Sum[Sum[Log[1/(1 - x)]^d/d, {d, Divisors[k]}] x^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%Y A322612 Cf. A227682, A265953, A322613.
%K A322612 nonn
%O A322612 0,3
%A A322612 _Ilya Gutkovskiy_, Dec 20 2018