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 A355113 #7 Jun 21 2022 12:46:30
%S A355113 1,2,13,133,1779,29565,589705,13728695,365295695,10934634985,
%T A355113 363678872325,13305294463275,531030788556475,22960273845453725,
%U A355113 1069101897816615425,53336480697298243375,2838300249311563302375,160480124820425410172625,9607441647405962075600125
%N A355113 Expansion of e.g.f. 5 / (6 - 5*x - exp(5*x)).
%F A355113 a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} binomial(n,k) * 5^(k-1) * a(n-k).
%F A355113 a(n) ~ n! / ((1 + LambertW(exp(6))) * ((6 - LambertW(exp(6)))/5)^(n+1)). - _Vaclav Kotesovec_, Jun 19 2022
%t A355113 nmax = 18; CoefficientList[Series[5/(6 - 5 x - Exp[5 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A355113 a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 5^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%Y A355113 Cf. A003577, A006155, A094418, A355110, A355111, A355112, A355114.
%K A355113 nonn
%O A355113 0,2
%A A355113 _Ilya Gutkovskiy_, Jun 19 2022