A367283 - OEIS

%I #9 Nov 12 2023 04:36:07

%S 1,1,4,20,116,728,4818,33100,233824,1687764,12393520,92291681,

%T 695325926,5290359124,40591599128,313725215636,2440203573816,

%U 19087022233906,150042056387660,1184734863936672,9392213303130904,74728563957003952,596531545003840160

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

%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=2, t=2, u=3) = 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. A002293, A073155, A214372, A367282.

%Y Cf. A001764, A137952.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 12 2023