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 A365569 #20 Nov 03 2024 11:28:11
%S A365569 1,3,27,387,7659,193491,5948091,215446563,8984708235,423944899443,
%T A365569 22328393101659,1298429924941251,82625791930962219,
%U A365569 5711012035686681363,426058604580805219323,34121803137713388036963,2919847869159667841599947,265868538017899566748612275
%N A365569 Expansion of e.g.f. 1 / (6 - 5 * exp(x))^(3/5).
%F A365569 a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+3)) * Stirling2(n,k).
%F A365569 a(0) = 1; a(n) = Sum_{k=1..n} (5 - 2*k/n) * binomial(n,k) * a(n-k).
%F A365569 a(n) ~ sqrt(2*Pi) * n^(n + 1/10) / (6^(3/5) * Gamma(3/5) * exp(n) * log(6/5)^(n + 3/5)). - _Vaclav Kotesovec_, Nov 11 2023
%F A365569 a(0) = 1; a(n) = 3*a(n-1) - 6*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Nov 16 2023
%t A365569 a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 11 2023 *)
%t A365569 With[{nn=20},CoefficientList[Series[1/(6-5*Exp[x])^(3/5),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 03 2024 *)
%o A365569 (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*stirling(n, k, 2));
%Y A365569 Cf. A094418, A346984, A365568, A365570.
%K A365569 nonn
%O A365569 0,2
%A A365569 _Seiichi Manyama_, Sep 09 2023