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 A381877 #10 Mar 09 2025 12:26:15
%S A381877 1,5,36,307,2891,29029,304716,3303712,36708842,415818822,4783832314,
%T A381877 55743318579,656528284027,7802975428711,93467830304056,
%U A381877 1127239608233884,13676060532043690,166800618473750824,2043978275887704674,25152767272402722288,310703538187552229521
%N A381877 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^4, where C(x) is the g.f. of A000108.
%F A381877 a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(5*n-5*k+3,n-k)/(n+k+1).
%F A381877 a(n) = binomial(3 + 5*n, n)*hypergeom([-3/4-n, -1/2-n, -1/4-n, -n, 1+n], [-3/5-n, -2/5-n, -1/5-n, 1/5-n], 2^8/5^5)/(1 + n). - _Stefano Spezia_, Mar 09 2025
%o A381877 (PARI) a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(5*n-5*k+3, n-k)/(n+k+1));
%Y A381877 Cf. A129442, A381875, A381876.
%Y A381877 Cf. A000108, A381861.
%K A381877 nonn
%O A381877 0,2
%A A381877 _Seiichi Manyama_, Mar 09 2025