A370478 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/3) / (1-x))^(3/2) )^3.

1, 3, 12, 46, 174, 654, 2451, 9177, 34368, 128826, 483531, 1817673, 6844294, 25815660, 97539435, 369154485, 1399419360, 5313440610, 20205330660, 76946898744, 293443125804, 1120565939780, 4284550682478, 16402204879386, 62864294076480, 241205747620740

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: B(x)^3 where B(x) is the g.f. of A071724.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1+x*((1-sqrt(1-4*x))/(2*x))^3)^3)
(PARI) a(n, r=3, s=3/2, t=3/2, 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, A370480.

Cf. A071724, A370477.

Sequence in context: A184699 A008781 A047013 * A108368 A264514 A344684

Adjacent sequences: A370475 A370476 A370477 * A370479 A370480 A370481

Keyword

nonn

Author

Seiichi Manyama, Mar 31 2024

Status

approved