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 A380171 #8 Jan 18 2025 09:28:06
%S A380171 1,1,5,31,265,2621,31621,85319,6574961,22334789,2092318021,
%T A380171 42552808871,187499032037,22150499622421,22390616112461,
%U A380171 15039597200385451,428293292251548001,103005657594642373,407547173842501629061,2708181047424714819491,36245898714951203790797
%N A380171 Numerators of coefficients in expansion of exp(-1 + 1 / Product_{k>=1} (1 - x^k)).
%F A380171 b(0) = 1, b(n) = (1/n) * Sum_{k=1..n} k * A000041(k) * b(n-k), a(n) = numerator of b(n).
%e A380171 1, 1, 5/2, 31/6, 265/24, 2621/120, 31621/720, 85319/1008, 6574961/40320, ...
%t A380171 nmax = 20; CoefficientList[Series[Exp[-1 + 1/Product[1 - x^k, {k, 1, nmax}]], {x, 0, nmax}], x] // Numerator
%t A380171 b[0] = 1; b[n_] := b[n] = (1/n) Sum[k PartitionsP[k] b[n - k], {k, 1, n}]; a[n_] := Numerator[b[n]]; Table[a[n], {n, 0, 20}]
%Y A380171 Cf. A000041, A017665, A058892, A066186, A067764, A098987, A380271 (denominators).
%K A380171 nonn,frac
%O A380171 0,3
%A A380171 _Ilya Gutkovskiy_, Jan 14 2025