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 A366012 #6 Sep 26 2023 03:53:30
%S A366012 1,2,13,156,2833,70098,2214280,85464984,3906724321,206648387550,
%T A366012 12425282899588,837384222603448,62539219710804627,5127758187193514824,
%U A366012 457986530357734020432,44263628968974498793648,4602969726808566383149761,512486177498084438210961270,60827938291895363867587959628
%N A366012 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+k,k) * binomial(n*(n+1),n-k).
%F A366012 a(n) = [x^n] (1/x) * Series_Reversion( x * (1 - x) / (1 + x)^n ).
%F A366012 a(n) ~ exp(n + 3/2) * n^(n - 3/2) / sqrt(2*Pi). - _Vaclav Kotesovec_, Sep 26 2023
%t A366012 Table[1/(n + 1) Sum[Binomial[n + k, n] Binomial[n (n + 1), n - k], {k, 0, n}], {n, 0, 18}]
%t A366012 Table[SeriesCoefficient[(1/x) InverseSeries[Series[x (1 - x)/(1 + x)^n, {x, 0, n + 1}], x], {x, 0, n}], {n, 0, 18}]
%Y A366012 Main diagonal of A107111.
%Y A366012 Cf. A000108, A006318, A062992, A135861, A263843, A365754, A365755.
%K A366012 nonn
%O A366012 0,2
%A A366012 _Ilya Gutkovskiy_, Sep 25 2023