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 A365765 #16 May 04 2025 15:11:09
%S A365765 1,5,39,365,3772,41491,476410,5644477,68493324,846937140,10633195119,
%T A365765 135185288475,1736883987836,22516798984946,294169295918996,
%U A365765 3869084306851933,51189853304834940,680816769653570044,9097058255214149068,122064057533865334100
%N A365765 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x) ).
%H A365765 Seiichi Manyama, <a href="/A365765/b365765.txt">Table of n, a(n) for n = 0..865</a>
%F A365765 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(5*n-k+3,n-k) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(n+1,n-k).
%t A365765 CoefficientList[(1/x) *InverseSeries[Series[x*(1-x)^4/(1+x),{x,0,20}]],x] (* _Stefano Spezia_, May 04 2025 *)
%o A365765 (PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(5*n-k+3, n-k))/(n+1);
%Y A365765 Cf. A003169, A006318, A365764, A365766.
%Y A365765 Cf. A365752.
%K A365765 nonn
%O A365765 0,2
%A A365765 _Seiichi Manyama_, Sep 18 2023