A371522 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^3.

1, 3, 24, 235, 2586, 30603, 380359, 4896753, 64731747, 873539236, 11984536632, 166661420814, 2343950447112, 33282048811530, 476462982915993, 6869620848003570, 99663539644072305, 1453861111238442363, 21312207036239313936, 313783619269186619589

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = 3 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+2,k)/(5*k+3).

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A349333.

Prog

(PARI) a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+2, k)/(5*k+3));

Crossrefs

Cf. A349333, A371379, A371519, A371521, A371523.

Sequence in context: A279651 A001099 A277462 * A230325 A363416 A365154

Adjacent sequences: A371519 A371520 A371521 * A371523 A371524 A371525

Keyword

nonn

Author

Seiichi Manyama, Mar 26 2024

Status

approved