A378411 G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x*A(x)^(3/2)) )^2.

1, 2, 3, 8, 19, 50, 137, 380, 1088, 3152, 9270, 27576, 82794, 250700, 764454, 2345688, 7237318, 22438988, 69876356, 218456216, 685400835, 2157396738, 6810801959, 21559694364, 68417766207, 217617573110, 693655532081, 2215401956720, 7088605614314, 22720370822508

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Formula

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

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A019497.

Prog

(PARI) a(n, r=2, s=1, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A371607, A371608.

Cf. A019497.

Sequence in context: A100342 A041281 A078343 * A148038 A326301 A148039

Adjacent sequences: A378408 A378409 A378410 * A378412 A378413 A378414

Keyword

nonn

Author

Seiichi Manyama, Dec 08 2024

Status

approved