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%I #23 Feb 16 2024 09:52:07
%S 1,1,5,17,83,381,1939,9905,52544,282315,1545130,8552557,47880020,
%T 270401515,1539288570,8821594865,50860072024,294774097800,
%U 1716506373521,10037592274363,58920231785426,347051995986538,2050627029532225,12151336260368205
%N Expansion of (1/x) * Series_Reversion( x*(1+x)^3*(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(3*n+k+2,k) * binomial(5*n-k+3,n-k).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(2*n-2*k,n-2*k). - _Seiichi Manyama_, Jan 18 2024
%F a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^3 * (1-x)^4 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*n+k+2, k)*binomial(5*n-k+3, n-k))/(n+1);
%o (SageMath)
%o def A365878(n):
%o h = binomial(5*n + 3, n) * hypergeometric([-n, 3*(n + 1)], [-5 * n - 3], -1) / (n + 1)
%o return simplify(h)
%o print([A365878(n) for n in range(24)]) # _Peter Luschny_, Sep 21 2023
%Y Cf. A365752, A365855.
%Y Cf. A365879, A368079.
%Y Cf. A370269.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 21 2023
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