A371516 - OEIS

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

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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.