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 A369512 #13 Mar 31 2025 22:01:42
%S A369512 1,8,106,1706,30459,580138,11548831,237408978,5001034821,107387829120,
%T A369512 2341915361920,51727723741200,1154821390130868,26016595619565008,
%U A369512 590718564607726952,13504019611821648448,310553715057038411358,7179645587769992602252
%N A369512 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x)^2 ).
%H A369512 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369512 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(7*n+2*k+5,n-k).
%t A369512 CoefficientList[InverseSeries[Series[x((1-x)^3-x)^2,{x,0,18}],x]/x,x] (* _Stefano Spezia_, Mar 31 2025 *)
%o A369512 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x)^2)/x)
%o A369512 (PARI) a(n) = sum(k=0, n, binomial(2*n+k+1, k)*binomial(7*n+2*k+5, n-k))/(n+1);
%Y A369512 Cf. A369215.
%K A369512 nonn
%O A369512 0,2
%A A369512 _Seiichi Manyama_, Jan 25 2024