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 A319219 #7 Jan 09 2019 09:19:25
%S A319219 1,-1,0,-3,32,-105,204,-3325,52408,-376425,1304180,-25766301,
%T A319219 659066484,-6675505837,30765540974,-893416597515,29169795361424,
%U A319219 -380344619169729,2379504317523300,-84225906785770525,3388223174832010540,-55107296201168047221,422923168260105913070
%N A319219 Expansion of e.g.f. Product_{k>=1} 1/(1 + x^k/(k - 1)!).
%F A319219 E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(-(j - 1)!)^k)).
%p A319219 seq(n!*coeff(series(mul(1/(1 + x^k/(k - 1)!),k=1..100),x=0,23),x,n),n=0..22); # _Paolo P. Lava_, Jan 09 2019
%t A319219 nmax = 22; CoefficientList[Series[Product[1/(1 + x^k/(k - 1)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A319219 nmax = 22; CoefficientList[Series[Exp[Sum[Sum[x^(j k)/(k (-(j - 1)!)^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A319219 a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[Sum[d (-(d - 1)!)^(-k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 22}]
%Y A319219 Cf. A032299, A076900, A076901, A292308, A319218.
%K A319219 sign
%O A319219 0,4
%A A319219 _Ilya Gutkovskiy_, Sep 13 2018