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 A354503 #16 Aug 16 2022 10:21:24
%S A354503 1,1,3,14,67,424,3093,26060,233917,2427224,27565317,339002146,
%T A354503 4450167269,63343680802,964189902141,15769859929260,270255218753593,
%U A354503 4913097747513800,94513145955643993,1904990351069631390,40153307898034641361,893402292594225679438
%N A354503 Expansion of e.g.f. ( Product_{k>0} (1 + x^k)^(1/k) )^exp(x).
%F A354503 a(0) = 1; a(n) = Sum_{k=1..n} A354506(k) * binomial(n-1,k-1) * a(n-k).
%o A354503 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k))^exp(x)))
%o A354503 (PARI) a354506(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1))/(k*(n-k)!));
%o A354503 a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354506(j)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y A354503 Cf. A347915, A354504.
%Y A354503 Cf. A354506, A356392.
%K A354503 nonn
%O A354503 0,3
%A A354503 _Seiichi Manyama_, Aug 15 2022