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 A356564 #13 Aug 13 2022 11:28:05
%S A356564 1,0,2,0,28,-30,888,-1260,51728,-196560,5293080,-22286880,710229408,
%T A356564 -4851269280,138348035616,-1091188098000,36482139114240,
%U A356564 -379928382462720,11812558481332992,-137793570801143040,4609972759421554560,-67292912045817561600
%N A356564 Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k) )^x.
%F A356564 a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * A048272(k-1)/(k-1) * binomial(n-1,k-1) * a(n-k).
%o A356564 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k))^x))
%o A356564 (PARI) a048272(n) = sumdiv(n, d, (-1)^(n/d+1));
%o A356564 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*a048272(j-1)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A356564 Cf. A356565, A356566.
%Y A356564 Cf. A007113, A048272, A338814, A356392.
%K A356564 sign
%O A356564 0,3
%A A356564 _Seiichi Manyama_, Aug 12 2022