login
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)^6).
2

%I #15 Aug 26 2023 08:56:24

%S 1,1,6,52,529,5889,69462,853013,10791018,139659604,1840435530,

%T 24611295075,333132371248,4555465710569,62839303262352,

%U 873363902976309,12218178082489873,171918448407833112,2431415226089290680,34544425914499450493,492807213597429920649

%N G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)^6).

%F a(n) = Sum_{k=0..n} binomial(6*n-k+1,k) * binomial(n-1,n-k)/(6*n-k+1).

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(5*n+2*k+1,k) * binomial(n-1,n-k)/(5*n+2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(6*n-k+1, k)*binomial(n-1, n-k)/(6*n-k+1));

%Y Cf. A002295, A243667, A349332, A364748, A365192, A365193.

%Y Cf. A219537, A271469, A364765.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 25 2023