A378787 - OEIS

%I #7 Dec 07 2024 10:41:43

%S 1,2,7,36,197,1184,7425,48308,322521,2198064,15227850,106924154,

%T 759245463,5442675080,39335090088,286296369000,2096706604597,

%U 15439417451928,114243931954962,849030345258990,6334510149389409,47428709540589036,356261301882333885

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

%F a(n) = Sum_{k=0..n} binomial(4*(n-k)+2,k) * binomial(3*k,n-k)/(2*(n-k)+1).

%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137957.

%o (PARI) a(n, r=2, s=3, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

%Y Cf. A069271, A371607, A371609.

%Y Cf. A137957.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 07 2024