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 A384413 #10 May 28 2025 09:19:13
%S A384413 1,37,33987,169103895,2499834885228,81779253109721484,
%T A384413 5002571587280667349252,513188808423273125116834036,
%U A384413 81795428604490137664191461936826,19140816569244304756404266108586220066,6295058477497449841660364475294196843864030,2810342651288539045376339873565157506716615522598
%N A384413 Expansion of Product_{k>=1} 1/(1 - k^3 * x)^((1/6) * (2/3)^k).
%F A384413 G.f.: exp((1/2) * Sum_{k>=1} b(3*k) * x^k/k), where b(n) = Sum_{k=0..n} 2^k * k! * Stirling2(n,k).
%o A384413 (PARI) b(n) = sum(k=0, n, 2^k*k!*stirling(n, k, 2));
%o A384413 my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, b(3*k)*x^k/k)/2))
%Y A384413 Cf. A004123, A090351.
%K A384413 nonn
%O A384413 0,2
%A A384413 _Seiichi Manyama_, May 28 2025