A378882 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)/(1 - x*A(x)^(5/3)) )^3.

1, 3, 15, 97, 717, 5736, 48340, 422688, 3799080, 34881159, 325750143, 3084634305, 29548452297, 285825135183, 2787990695931, 27391816756281, 270828413410413, 2692692976016352, 26904718314949776, 270017389769189136, 2720718671661444780, 27513054621821846074

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

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

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

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).

Prog

(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));

Crossrefs

Cf. A349017, A378801, A378828.

Cf. A378883.

Sequence in context: A262751 A378890 A231445 * A108442 A060148 A143435

Adjacent sequences: A378879 A378880 A378881 * A378883 A378884 A378885

Keyword

nonn

Author

Seiichi Manyama, Dec 09 2024

Status

approved