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 A323216 #7 Jul 21 2019 04:23:00
%S A323216 1,1,7,56,477,4180,37401,339184,3107583,28691938,266537777,2488340790,
%T A323216 23326071990,219416722056,2070014554612,19578402111888,
%U A323216 185583671757949,1762564846962972,16768616366059543,159777503753057786,1524516616304476102,14564266581096857240
%N A323216 Main diagonal of A323212.
%t A323216 nmax = 21; T = PadRight[CoefficientList[# + O[y]^(nmax+1), y], nmax+1]& /@ CoefficientList[1 + 2 x (x+1)/(Sqrt[1 - 4 y] - 2 x (x+1) + 1) + O[x]^(nmax+1), x];
%t A323216 a[n_] := T[[n + 1, n + 1]];
%t A323216 Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Jul 21 2019 *)
%Y A323216 A323212.
%K A323216 nonn
%O A323216 0,3
%A A323216 _Peter Luschny_, Mar 18 2019