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 A365855 #21 Feb 16 2024 09:53:30
%S A365855 1,2,9,46,264,1612,10291,67830,458109,3153744,22049065,156127140,
%T A365855 1117369884,8069610992,58735003740,430416574918,3172987081311,
%U A365855 23514565653058,175083678670264,1309132916709168,9825882638364144,74003924059921940,559112987425763365
%N A365855 Expansion of (1/x) * Series_Reversion( x*(1+x)^2*(1-x)^4 ).
%H A365855 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A365855 a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(2*n+k+1,k) * binomial(5*n-k+3,n-k).
%F A365855 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(3*n-2*k+1,n-2*k). - _Seiichi Manyama_, Jan 18 2024
%F A365855 a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^2 * (1-x)^4 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A365855 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k+1, k)*binomial(5*n-k+3, n-k))/(n+1);
%o A365855 (SageMath)
%o A365855 def A365855(n):
%o A365855 h = binomial(5*n + 3, n) * hypergeometric([-n, 2*n + 2], [-5 * n - 3], -1) / (n + 1)
%o A365855 return simplify(h)
%o A365855 print([A365855(n) for n in range(23)]) # _Peter Luschny_, Sep 20 2023
%Y A365855 Cf. A365854, A365856.
%Y A365855 Cf. A365752, A368967.
%K A365855 nonn
%O A365855 0,2
%A A365855 _Seiichi Manyama_, Sep 20 2023