A378731 G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)^(4/3)) )^3.

1, 3, 6, 22, 93, 417, 1993, 9864, 50217, 261239, 1382448, 7418877, 40278175, 220830513, 1220930337, 6799458685, 38107621704, 214771481163, 1216457185122, 6920603372448, 39529745832681, 226605757331904, 1303291125124071, 7518151040142000, 43488151271999326

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f.: A(x) = (1 + x*B(x))^3 where B(x) is the g.f. of A364743.

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=0, u=4) = 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. A364743, A371612, A378732.

Sequence in context: A209067 A220166 A220167 * A243336 A344605 A029848

Adjacent sequences: A378728 A378729 A378730 * A378732 A378733 A378734

Keyword

nonn

Author

Seiichi Manyama, Dec 05 2024

Status

approved