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 A365856 #20 Feb 16 2024 09:52:12
%S A365856 1,3,17,115,863,6903,57687,497683,4398980,39630305,362562226,
%T A365856 3359252039,31457036708,297247495745,2830725974514,27140465365203,
%U A365856 261768686779800,2538061348959000,24724191398850125,241862002342417585,2374978445599884762
%N A365856 Expansion of (1/x) * Series_Reversion( x*(1+x)^2*(1-x)^5 ).
%H A365856 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A365856 a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(2*n+k+1,k) * binomial(6*n-k+4,n-k).
%F A365856 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(4*n-2*k+2,n-2*k). - _Seiichi Manyama_, Jan 18 2024
%F A365856 a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^2 * (1-x)^5 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A365856 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k+1, k)*binomial(6*n-k+4, n-k))/(n+1);
%o A365856 (SageMath)
%o A365856 def A365856(n):
%o A365856 h = binomial(6*n + 4, n) * hypergeometric([-n, 2*n + 2], [-6 * n - 4], -1) / (n + 1)
%o A365856 return simplify(h)
%o A365856 print([A365856(n) for n in range(21)]) # _Peter Luschny_, Sep 20 2023
%Y A365856 Cf. A365854, A365855.
%Y A365856 Cf. A365753.
%K A365856 nonn
%O A365856 0,2
%A A365856 _Seiichi Manyama_, Sep 20 2023