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 A365600 #13 Nov 10 2023 08:04:08
%S A365600 1,3,18,174,2292,38292,774624,18399840,501868416,15456483840,
%T A365600 530462128896,20073406663296,830293158570624,37267057695192192,
%U A365600 1803930663341528064,93672204405378891264,5193925606670524254720,306280622206497897745920
%N A365600 Expansion of e.g.f. 1 / (1 - 4 * log(1 + x))^(3/4).
%F A365600 a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (4*j+3)) * Stirling1(n,k).
%F A365600 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (4 - k/n) * (k-1)! * binomial(n,k) * a(n-k).
%F A365600 a(n) ~ Gamma(1/4) * n^(n + 1/4) / (2^(3/2) * sqrt(Pi) * (exp(1/4) - 1)^(n + 3/4) * exp(n - 3/16)). - _Vaclav Kotesovec_, Nov 10 2023
%t A365600 a[n_] := Sum[Product[4*j + 3, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 13 2023 *)
%o A365600 (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 4*j+3)*stirling(n, k, 1));
%Y A365600 Cf. A347021, A354147, A354240.
%Y A365600 Cf. A365584.
%K A365600 nonn
%O A365600 0,2
%A A365600 _Seiichi Manyama_, Sep 11 2023