A367260 - OEIS

%I #7 Nov 11 2023 13:55:38

%S 1,1,6,36,251,1881,14817,120950,1014042,8680377,75552553,666614637,

%T 5948817600,53599239101,486926148000,4455202562652,41018936164660,

%U 379747493741643,3532914858433284,33012260400580342,309692626084981245,2915659701275923491

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

%F If g.f. satisfies A(x) = 1 + x*A(x)^t * (1 + x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(s*k,n-k) / (t*k+u*(n-k)+1).

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

%Y Cf. A019497, A361305, A364742.

%Y Cf. A367233.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 11 2023