A367261 - OEIS

%I #8 Nov 11 2023 13:55:33

%S 1,1,4,16,77,393,2113,11761,67217,392140,2325691,13980390,84990482,

%T 521623164,3227679457,20114056545,126125100615,795207084713,

%U 5038166859565,32059491655921,204806561028553,1313023485343009,8445060537757367,54476991669555231

%N G.f. satisfies A(x) = 1 + x*A(x) * (1 + x*A(x)^2)^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=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. A137953, A367239.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 11 2023