A367258 - OEIS

%I #10 Nov 11 2023 13:55:29

%S 1,1,3,10,39,162,708,3202,14867,70448,339324,1656443,8176968,40749277,

%T 204727198,1035837256,5273360195,26992906495,138840628986,

%U 717245323961,3719765478096,19359725932165,101083353127371,529341453000447,2779470724644476,14630696492685339

%N G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^2)^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=1, u=2) = 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. A000108.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 11 2023