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%I #23 Feb 16 2024 09:53:42
%S 1,3,16,103,735,5592,44452,364815,3067558,26290517,228819168,
%T 2016953848,17968790029,161536295244,1463535347928,13349907110367,
%U 122499957767130,1130001670577730,10472708110616136,97468774074103041,910582642690819351
%N Expansion of (1/x) * Series_Reversion( x*(1+x)*(1-x)^4 ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(n+k,k) * binomial(5*n-k+3,n-k).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(4*n-2*k+2,n-2*k). - _Seiichi Manyama_, Jan 18 2024
%F a(n) = (1/(n+1)) * [x^n] 1/( (1+x) * (1-x)^4 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(5*n-k+3, n-k))/(n+1);
%o (SageMath)
%o def A365752(n):
%o h = binomial(5*n + 3, n) * hypergeometric([-n, n + 1], [-5 * n - 3], -1) / (n + 1)
%o return simplify(h)
%o print([A365752(n) for n in range(21)]) # _Peter Luschny_, Sep 20 2023
%Y Cf. A063020, A365751, A365753.
%Y Cf. A365856, A368079.
%Y Cf. A365754, A370105.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 18 2023
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