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 A381827 #9 Mar 08 2025 09:39:48
%S A381827 1,2,10,69,562,5042,48100,478547,4908338,51522174,550758208,
%T A381827 5974753990,65608248500,727835313461,8144965594184,91834891588099,
%U A381827 1042244963201914,11896871741939462,136493661712053752,1573151972820654218,18205626549920314728,211468167403628323318
%N A381827 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108.
%F A381827 a(n) = Sum_{k=0..n} binomial(3*n-k+1,k) * binomial(4*n-4*k,n-k)/(3*n-k+1).
%o A381827 (PARI) a(n) = sum(k=0, n, binomial(3*n-k+1, k)*binomial(4*n-4*k, n-k)/(3*n-k+1));
%Y A381827 Cf. A014137, A129442, A381826.
%Y A381827 Cf. A000108, A381782.
%K A381827 nonn
%O A381827 0,2
%A A381827 _Seiichi Manyama_, Mar 08 2025