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 A379090 #10 Dec 15 2024 07:25:29
%S A379090 1,1,3,13,69,409,2578,16883,113606,780710,5457275,38687680,277511415,
%T A379090 2010540125,14690727157,108136401031,801111528944,5968615651663,
%U A379090 44692765261977,336164201398198,2538745667960316,19242953564513454,146340183680256968,1116267947369766774
%N A379090 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x^3*A(x)^10).
%F A379090 G.f. A(x) satisfies A(x) = exp( 1/3 * Sum_{k>=1} A379087(k) * x^k/k ).
%F A379090 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k+1,k) * binomial(3*n+k+1,n-3*k)/(3*n+k+1) = (1/(3*n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k,k) * binomial(3*n+k+1,n-3*k).
%o A379090 (PARI) a(n) = sum(k=0, n\3, binomial(3*n+k+1, k)*binomial(3*n+k+1, n-3*k)/(3*n+k+1));
%Y A379090 Cf. A379087.
%K A379090 nonn
%O A379090 0,3
%A A379090 _Seiichi Manyama_, Dec 15 2024