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 A368961 #20 Aug 11 2025 10:20:44
%S A368961 1,2,9,48,286,1820,12116,83334,587537,4223582,30840355,228111390,
%T A368961 1705509981,12868775056,97867753424,749401318160,5772939358590,
%U A368961 44708058004740,347879528717526,2718400037837988,21323471768334120,167844335760482220,1325332432687278960
%N A368961 Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^2 ).
%H A368961 Seiichi Manyama, <a href="/A368961/b368961.txt">Table of n, a(n) for n = 0..1000</a>
%H A368961 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A368961 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(3*n-k+1,n-2*k).
%t A368961 a[n_] := (1/(n+1)) * Sum[Binomial[2*n+k+1,k] * Binomial[3*n-k+1,n-2*k],{k,0,Floor[n/2]}]; Array[a,23,0] (* _Stefano Spezia_, Aug 11 2025 *)
%o A368961 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^2)/x)
%o A368961 (PARI) a(n, s=2, t=2, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y A368961 Cf. A368965, A368967.
%Y A368961 Cf. A001002.
%K A368961 nonn
%O A368961 0,2
%A A368961 _Seiichi Manyama_, Jan 10 2024