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 A365879 #22 Feb 16 2024 09:52:04
%S A365879 1,2,10,54,332,2162,14734,103630,746857,5486206,40926152,309202686,
%T A365879 2361065920,18192978966,141280871840,1104603758526,8687878404289,
%U A365879 68692224882620,545681467048132,4353096328518810,34858239962177764,280095777427596008
%N A365879 Expansion of (1/x) * Series_Reversion( x*(1+x)^3*(1-x)^5 ).
%H A365879 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A365879 a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(3*n+k+2,k) * binomial(6*n-k+4,n-k).
%F A365879 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(3*n-2*k+1,n-2*k). - _Seiichi Manyama_, Jan 18 2024
%F A365879 a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^3 * (1-x)^5 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A365879 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*n+k+2, k)*binomial(6*n-k+4, n-k))/(n+1);
%o A365879 (SageMath)
%o A365879 def A365879(n):
%o A365879 h = binomial(6*n + 4, n) * hypergeometric([-n, 3*(n + 1)], [-6 * n - 4], -1) / (n + 1)
%o A365879 return simplify(h)
%o A365879 print([A365879(n) for n in range(22)]) # _Peter Luschny_, Sep 21 2023
%Y A365879 Cf. A365753, A365856, A365880.
%Y A365879 Cf. A365878, A368079.
%Y A365879 Cf. A370270.
%K A365879 nonn
%O A365879 0,2
%A A365879 _Seiichi Manyama_, Sep 21 2023