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 A365764 #16 May 04 2025 16:34:33
%S A365764 1,4,25,188,1563,13840,127972,1221260,11938471,118936100,1203155633,
%T A365764 12325599632,127611357300,1333153669632,14035828918560,
%U A365764 148773617605036,1586305110768863,17002975960876300,183102052226442475,1980078493171083292,21493846031259095539
%N A365764 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1+x) ).
%H A365764 Seiichi Manyama, <a href="/A365764/b365764.txt">Table of n, a(n) for n = 0..940</a>
%F A365764 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(4*n-k+2,n-k) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(n+1,n-k).
%t A365764 CoefficientList[(1/x) *InverseSeries[Series[x*(1-x)^3/(1+x),{x,0,21}]],x] (* _Stefano Spezia_, May 04 2025 *)
%o A365764 (PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(4*n-k+2, n-k))/(n+1);
%Y A365764 Cf. A003169, A006318, A365765, A365766.
%Y A365764 Cf. A365751.
%K A365764 nonn
%O A365764 0,2
%A A365764 _Seiichi Manyama_, Sep 18 2023