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 A369296 #15 Feb 15 2024 04:23:16
%S A369296 1,1,2,7,24,84,315,1225,4859,19646,80739,336050,1413587,6000777,
%T A369296 25674462,110598855,479286932,2088036939,9139604421,40174594432,
%U A369296 177267942918,784889441217,3486198469890,15529021825140,69355660644738,310509670642611,1393296782758244
%N A369296 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x^3)^2 ).
%H A369296 P. Bala, <a href="/A251592/a251592.pdf">Fractional iteration of a series inversion operator</a>
%H A369296 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369296 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(2*n-3*k,n-3*k).
%F A369296 a(n) = (1/(n+1)) * [x^n] 1/( (1-x) * (1-x^3)^2 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369296 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x^3)^2)/x)
%o A369296 (PARI) a(n, s=3, t=2, u=1) = 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 A369296 Cf. A063030, A369299.
%Y A369296 Cf. A370274.
%K A369296 nonn
%O A369296 0,3
%A A369296 _Seiichi Manyama_, Jan 18 2024