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 A321798 #35 Nov 05 2021 13:11:12
%S A321798 1,1,5,23,117,636,3607,21106,126489,772468,4789844,30075937,190851839,
%T A321798 1222000222,7885041530,51222338580,334720178969,2198755865424,
%U A321798 14511029102232,96169424666028,639757737711300,4270520564506069,28595671605541357,192025292117465445,1292866976587651519
%N A321798 G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4).
%H A321798 Seiichi Manyama, <a href="/A321798/b321798.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..199 from Ludovic Schwob)
%F A321798 a(n) = Sum_{k=0..n} (C(n,k)/(n-k+1)) * C(n+3*k-1,n-k).
%F A321798 a(n) ~ sqrt((1 - r*s)*(1 + 3*r*s)/(8*Pi*(8*s - 3))) / (n^(3/2) * r^(n+1)), where r = 0.139684805934917057093949761392656080860096066578... and s = 1.76437708701490464570032194388560298744432681226... are real roots of the system of equations s*(1 - r/(1 - r*s)^4) = 1, 4*r^2*s^2 = (1 - r*s)^5. - _Vaclav Kotesovec_, Nov 21 2018
%t A321798 a[n_] := Sum[Binomial[n, k] * Binomial[n + 3k - 1, n - k]/(n - k + 1), {k, 0,
%t A321798 n}]; Array[a, 20, 0] (* _Amiram Eldar_, Nov 19 2018 *)
%o A321798 (PARI) a(n) = sum(k=0, n, binomial(n,k)*binomial(n+3*k-1, n-k)/(n-k+1)); \\ _Michel Marcus_, Nov 19 2018
%o A321798 (GAP) List([0..25],n->Sum([0..n],k->Binomial(n,k)/(n-k+1)*Binomial(n+3*k-1,n-k))); # _Muniru A Asiru_, Nov 24 2018
%Y A321798 Cf. A109081, A161797, A321799.
%K A321798 nonn
%O A321798 0,3
%A A321798 _Ludovic Schwob_, Nov 19 2018