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 A365854 #18 Feb 16 2024 09:53:34
%S A365854 1,1,4,13,55,232,1052,4869,23206,112519,554560,2767336,13959941,
%T A365854 71060356,364569352,1883143669,9785481498,51118097686,268294595396,
%U A365854 1414106565611,7481787454031,39721596068000,211549545257760,1129912319370600,6050931114958080
%N A365854 Expansion of (1/x) * Series_Reversion( x*(1+x)^2*(1-x)^3 ).
%H A365854 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A365854 a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(2*n+k+1,k) * binomial(4*n-k+2,n-k).
%F A365854 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(2*n-2*k,n-2*k). - _Seiichi Manyama_, Jan 18 2024
%F A365854 a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^2 * (1-x)^3 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A365854 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k+1, k)*binomial(4*n-k+2, n-k))/(n+1);
%o A365854 (SageMath)
%o A365854 def A365854(n):
%o A365854 h = binomial(2*(2*n + 1), n) * hypergeometric([-n, 2*(n + 1)], [-2*(2*n + 1)], -1) / (n + 1)
%o A365854 return simplify(h)
%o A365854 print([A365854(n) for n in range(25)]) # _Peter Luschny_, Sep 20 2023
%Y A365854 Cf. A365855, A365856.
%Y A365854 Cf. A063020, A365878, A365880.
%Y A365854 Cf. A365751, A370103.
%K A365854 nonn
%O A365854 0,3
%A A365854 _Seiichi Manyama_, Sep 20 2023