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 A365567 #19 Nov 16 2023 11:50:23
%S A365567 1,3,24,297,5001,106578,2748399,83182347,2890153626,113364686403,
%T A365567 4954547485149,238734066994272,12573018414279501,718498413957515103,
%U A365567 44278797576715884024,2927171415480872824197,206625238881832412874501,15511299587628626891270178
%N A365567 Expansion of e.g.f. 1 / (5 - 4 * exp(x))^(3/4).
%F A365567 a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k).
%F A365567 a(0) = 1; a(n) = Sum_{k=1..n} (4 - k/n) * binomial(n,k) * a(n-k).
%F A365567 a(n) ~ Gamma(1/4) * n^(n + 1/4) / (5^(3/4) * sqrt(Pi) * exp(n) * log(5/4)^(n + 3/4)). - _Vaclav Kotesovec_, Nov 11 2023
%F A365567 a(0) = 1; a(n) = 3*a(n-1) - 5*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Nov 16 2023
%t A365567 a[n_] := Sum[Product[4*j + 3, {j, 0, k - 1}] * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 11 2023 *)
%o A365567 (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 4*j+3)*stirling(n, k, 2));
%Y A365567 Cf. A094417, A346983, A354242.
%K A365567 nonn
%O A365567 0,2
%A A365567 _Seiichi Manyama_, Sep 09 2023