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 A355114 #7 Jun 21 2022 12:45:58
%S A355114 1,2,14,156,2256,40416,869040,21817440,626063616,20210176512,
%T A355114 724888631808,28599923045376,1230970377166848,57397448756994048,
%U A355114 2882187551571941376,155065468075097960448,8898907099302329647104,542609247778976191610880,35031706496702707368591360
%N A355114 Expansion of e.g.f. 6 / (7 - 6*x - exp(6*x)).
%F A355114 a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} binomial(n,k) * 6^(k-1) * a(n-k).
%F A355114 a(n) ~ n! / ((1 + LambertW(exp(7))) * ((7 - LambertW(exp(7)))/6)^(n+1)). - _Vaclav Kotesovec_, Jun 19 2022
%t A355114 nmax = 18; CoefficientList[Series[6/(7 - 6 x - Exp[6 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A355114 a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 6^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%Y A355114 Cf. A003578, A006155, A094419, A355110, A355111, A355112, A355113.
%K A355114 nonn
%O A355114 0,2
%A A355114 _Ilya Gutkovskiy_, Jun 19 2022