A378882 - OEIS

%I #12 Dec 10 2024 05:56:32

%S 1,3,15,97,717,5736,48340,422688,3799080,34881159,325750143,

%T 3084634305,29548452297,285825135183,2787990695931,27391816756281,

%U 270828413410413,2692692976016352,26904718314949776,270017389769189136,2720718671661444780,27513054621821846074

%N G.f. A(x) satisfies A(x) = ( 1 + x*A(x)/(1 - x*A(x)^(5/3)) )^3.

%F G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^(2/3)/(1 - x*A(x)^(5/3)) )^3.

%F G.f. A(x) satisfies A(x) = 1 + x * A(x) * (1 + A(x)^(1/3) + A(x)^(5/3)).

%F G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A378883.

%F If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

%o (PARI) a(n, r=3, s=1, t=3, u=5) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

%Y Cf. A349017, A378801, A378828.

%Y Cf. A378883.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 09 2024