A366176 - OEIS

%I #9 Oct 03 2023 08:59:35

%S 1,1,5,27,161,1030,6921,48190,344669,2517303,18695908,140771477,

%T 1072130229,8244820518,63931532190,499308229278,3924204043333,

%U 31012883225891,246304580923299,1964794017165157,15735626383151876,126476316316459089,1019883740031357941

%N G.f. A(x) satisfies A(x) = 1 + x*A(x)^3/(1 - x)^2.

%F a(n) = Sum_{k=0..n} binomial(n+k-1,n-k) * binomial(3*k,k)/(2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+k-1, n-k)*binomial(3*k, k)/(2*k+1));

%Y Partial sums give A199475.

%Y Cf. A001764, A213282, A307678.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 03 2023