A378153 G.f. A(x) satisfies A(x) = 1 + (x * (1+x))^3 * A(x)^2.

1, 0, 0, 1, 3, 3, 3, 12, 30, 45, 75, 192, 436, 798, 1554, 3542, 7740, 15543, 32183, 70794, 153252, 321431, 684123, 1491504, 3232672, 6928779, 14957787, 32615388, 70991040, 153985890, 335256886, 733206840, 1603258134, 3503385568, 7671749664, 16837946850

Offset

0,5

Links

Table of n, a(n) for n=0..35.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*k,n-3*k) * C(k), where C(k) are the Catalan numbers (A000108).

G.f.: 2/(1 + sqrt(1 - 4*(x*(1+x))^3)).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(3*k, n-3*k)*binomial(2*k, k)/(k+1));

Crossrefs

Cf. A115055, A378151.

Cf. A000108.

Sequence in context: A052900 A024947 A291407 * A147823 A341211 A335518

Adjacent sequences: A378150 A378151 A378152 * A378154 A378155 A378156

Keyword

nonn

Author

Seiichi Manyama, Nov 18 2024

Status

approved