A378155 - OEIS

%I #5 Nov 18 2024 09:45:03

%S 1,6,48,452,4680,51504,591312,7002864,84926304,1049402944,13165069824,

%T 167239042176,2146912312064,27808372643328,362981425115904,

%U 4769884412086016,63050983340533248,837805424714425344,11184489029495865344,149935005483457542144,2017560365768892739584

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

%F G.f.: B(x)^3 where B(x) is the g.f. of A219534.

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

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

%Y Cf. A219534, A371693, A378156.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 18 2024