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 A368079 #42 Feb 16 2024 09:51:55
%S A368079 1,3,18,127,996,8322,72644,654615,6043455,56866028,543368586,
%T A368079 5258196762,51426990112,507537393600,5048033356128,50549237164615,
%U A368079 509197913456922,5156339940802941,52460340305220466,535976129228082972,5496745175387480976
%N A368079 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 * (1-x^2)^3 ).
%H A368079 Seiichi Manyama, <a href="/A368079/b368079.txt">Table of n, a(n) for n = 0..963</a>
%H A368079 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A368079 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(4*n-2*k+2,n-2*k).
%F A368079 a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(3*n+k+2,k) * binomial(7*n-k+5,n-k).
%F A368079 a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^3 * (1-x)^6 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A368079 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3*(1-x^2)^3)/x)
%o A368079 (PARI) a(n, s=2, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
%Y A368079 Cf. A365752, A365856.
%Y A368079 Cf. A365878, A365879.
%Y A368079 Cf. A130565, A369301.
%Y A368079 Cf. A369264, A370271.
%K A368079 nonn
%O A368079 0,2
%A A368079 _Seiichi Manyama_, Jan 18 2024