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 A380271 #4 Jan 18 2025 09:28:17
%S A380271 1,1,2,6,24,120,720,1008,40320,72576,3628800,39916800,95800320,
%T A380271 6227020800,3487131648,1307674368000,20922789888000,2845499424768,
%U A380271 6402373705728000,24329020081766400,187146308321280000,51090942171709440000,224800145555521536000,25852016738884976640000
%N A380271 Denominators of coefficients in expansion of exp(-1 + 1 / Product_{k>=1} (1 - x^k)).
%F A380271 b(0) = 1, b(n) = (1/n) * Sum_{k=1..n} k * A000041(k) * b(n-k), a(n) = denominator of b(n).
%e A380271 1, 1, 5/2, 31/6, 265/24, 2621/120, 31621/720, 85319/1008, 6574961/40320, ...
%t A380271 nmax = 23; CoefficientList[Series[Exp[-1 + 1/Product[1 - x^k, {k, 1, nmax}]], {x, 0, nmax}], x] // Denominator
%t A380271 b[0] = 1; b[n_] := b[n] = (1/n) Sum[k PartitionsP[k] b[n - k], {k, 1, n}]; a[n_] := Denominator[b[n]]; Table[a[n], {n, 0, 23}]
%Y A380271 Cf. A000041, A017666, A058892, A066186, A067653, A098988, A380171 (numerators).
%K A380271 nonn,frac
%O A380271 0,3
%A A380271 _Ilya Gutkovskiy_, Jan 18 2025