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 A365584 #14 Nov 11 2023 05:04:16
%S A365584 1,3,24,300,5100,109692,2854344,87164088,3055516800,120916282368,
%T A365584 5331444120576,259168711406976,13769882994784896,793844510730348672,
%U A365584 49353915922852214016,3291455140392403401984,234388011123877880424960,17750517946502792294592000
%N A365584 Expansion of e.g.f. 1 / (1 + 4 * log(1-x))^(3/4).
%F A365584 a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (4*j+3)) * |Stirling1(n,k)|.
%F A365584 a(0) = 1; a(n) = Sum_{k=1..n} (4 - k/n) * (k-1)! * binomial(n,k) * a(n-k).
%F A365584 a(n) ~ Gamma(1/4) * n^(n + 1/4) / (2^(3/2) * sqrt(Pi) * (exp(1/4) - 1)^(n + 3/4) * exp(3*n/4)). - _Vaclav Kotesovec_, Nov 11 2023
%t A365584 a[n_] := Sum[Product[4*j + 3, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 10 2023 *)
%o A365584 (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 4*j+3)*abs(stirling(n, k, 1)));
%Y A365584 Cf. A347016, A354241, A354264.
%Y A365584 Cf. A365567.
%K A365584 nonn
%O A365584 0,2
%A A365584 _Seiichi Manyama_, Sep 10 2023