A366238 - OEIS

%I #9 Oct 05 2023 08:35:09

%S 1,2,8,42,224,1281,7630,46816,294008,1880588,12209474,80251889,

%T 532988530,3571260662,24112334292,163887278097,1120445503036,

%U 7699924478714,53160597794588,368549236730128,2564649436452878,17907555498455680,125426544531794332

%N G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^4*A(x)^2.

%F G.f.: 2*(1+x) / (1 + sqrt(1-4*x*(1+x)^5)).

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

%o (PARI) a(n) = sum(k=0, n, binomial(5*k+1, n-k)*binomial(2*k, k)/(k+1));

%Y Cf. A073157, A366236, A366237.

%Y Cf. A000108.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 05 2023