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 A369215 #17 Mar 31 2025 22:01:25
%S A369215 1,4,29,261,2627,28315,319648,3731037,44663058,545312504,6764556591,
%T A369215 85015779095,1080185111768,13852183882612,179058158369828,
%U A369215 2330621446075640,30519758687849439,401806204894374041,5315243189757111099,70613088335938995385,941714812929017751855
%N A369215 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x) ).
%H A369215 Seiichi Manyama, <a href="/A369215/b369215.txt">Table of n, a(n) for n = 0..868</a>
%H A369215 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369215 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+k,k) * binomial(4*n+2*k+2,n-k).
%t A369215 CoefficientList[InverseSeries[Series[x((1-x)^3-x),{x,0,21}],x]/x,x] (* _Stefano Spezia_, Mar 31 2025 *)
%o A369215 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x))/x)
%o A369215 (PARI) a(n) = sum(k=0, n, binomial(n+k, k)*binomial(4*n+2*k+2, n-k))/(n+1);
%Y A369215 Cf. A369114, A369161.
%Y A369215 Cf. A151374, A249924, A369216.
%Y A369215 Cf. A365764, A379171, A379172.
%Y A369215 Cf. A049140.
%K A369215 nonn
%O A369215 0,2
%A A369215 _Seiichi Manyama_, Jan 16 2024