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 A365878 #23 Feb 16 2024 09:52:07
%S A365878 1,1,5,17,83,381,1939,9905,52544,282315,1545130,8552557,47880020,
%T A365878 270401515,1539288570,8821594865,50860072024,294774097800,
%U A365878 1716506373521,10037592274363,58920231785426,347051995986538,2050627029532225,12151336260368205
%N A365878 Expansion of (1/x) * Series_Reversion( x*(1+x)^3*(1-x)^4 ).
%H A365878 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A365878 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 A365878 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 A365878 a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^3 * (1-x)^4 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A365878 (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 A365878 (SageMath)
%o A365878 def A365878(n):
%o A365878 h = binomial(5*n + 3, n) * hypergeometric([-n, 3*(n + 1)], [-5 * n - 3], -1) / (n + 1)
%o A365878 return simplify(h)
%o A365878 print([A365878(n) for n in range(24)]) # _Peter Luschny_, Sep 21 2023
%Y A365878 Cf. A365752, A365855.
%Y A365878 Cf. A365879, A368079.
%Y A365878 Cf. A370269.
%K A365878 nonn
%O A365878 0,3
%A A365878 _Seiichi Manyama_, Sep 21 2023