A371516 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^3.

1, 3, 15, 82, 477, 2901, 18235, 117555, 773085, 5166478, 34987170, 239570655, 1655933060, 11538839130, 80971109712, 571702698185, 4058556404958, 28951715755830, 207424064434502, 1491898838023884, 10768487956456506, 77977009814421534, 566310026687320290

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = 3 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(3*k+2,k)/(2*k+3) = Sum_{k=0..n} binomial(n-1,n-k) * binomial(3*k+3,k)/(k+1).

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A307678.

Prog

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

Crossrefs

Cf. A045868, A371517, A371520, A371521.

Cf. A270386, A307678.

Cf. A371483.

Sequence in context: A343975 A255676 A015680 * A084208 A059271 A345885

Adjacent sequences: A371513 A371514 A371515 * A371517 A371518 A371519

Keyword

nonn

Author

Seiichi Manyama, Mar 26 2024

Status

approved