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 A369013 #19 Jan 25 2024 06:54:05
%S A369013 1,0,3,3,27,60,355,1128,5694,21610,102462,426465,1978547,8659386,
%T A369013 40003167,180241995,834994605,3830870574,17841265598,82854767805,
%U A369013 388124777739,1818343250570,8565240659274,40398758877564,191254160050512,906956708168838,4312790630717025
%N A369013 Expansion of (1/x) * Series_Reversion( x * (1-x^2/(1-x))^3 ).
%C A369013 Satisfies a 7-term D-finite recurrence with 7-order polynomials. - _R. J. Mathar_, Jan 25 2024
%H A369013 Seiichi Manyama, <a href="/A369013/b369013.txt">Table of n, a(n) for n = 0..1000</a>
%H A369013 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369013 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(n-k-1,n-2*k).
%o A369013 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x^2/(1-x))^3)/x)
%o A369013 (PARI) a(n, s=2, t=3, u=-3) = 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 A369013 Cf. A369012, A369014.
%K A369013 nonn
%O A369013 0,3
%A A369013 _Seiichi Manyama_, Jan 11 2024