A370480 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/3) / (1-x))^2 )^3.

1, 3, 15, 73, 360, 1800, 9112, 46632, 240936, 1255336, 6589080, 34811784, 184990568, 988156872, 5303039256, 28579068520, 154605138984, 839272725864, 4570409517848, 24961191298248, 136688674353000, 750355591919240, 4128471397725336, 22762905189252264

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: B(x)^3 where B(x) is the g.f. of A006319.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1+x*((1-x-sqrt(1-6*x+x^2))/(2*x))^2)^3)
(PARI) a(n, r=3, s=2, t=2, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A058396, A370478.

Cf. A006319, A370479.

Sequence in context: A156019 A145839 A232289 * A055837 A124543 A007142

Adjacent sequences: A370477 A370478 A370479 * A370481 A370482 A370483

Keyword

nonn

Author

Seiichi Manyama, Mar 31 2024

Status

approved