A386392 a(n) = 4 * binomial(7*n+4,n)/(7*n+4).

1, 4, 34, 368, 4495, 59052, 814506, 11633440, 170574723, 2552698720, 38832808586, 598724403680, 9335085772194, 146936230074004, 2331703871687400, 37263447339612480, 599206511767593099, 9688121925389895636, 157401957319775436400, 2568427016865897264000

Offset: 0

Author

Seiichi Manyama, Jul 20 2025

Keywords

• nonn

Links

• Wikipedia, Fuss-Catalan number

Crossrefs

Cf. A118971, A212073, A234463, A234507, A234527, A234870.

Cf. A002296, A386380.

Programs

PARI

apr(n, p, r) = r*binomial(n*p+r, n)/(n*p+r);
a(n) = apr(n, 7, 4);

Formula

a(n) = r * binomial(n*p+r,n)/(n*p+r), the Fuss-Catalan number with p=7 and r=4.

a(n) = A386380(6*n+3).

G.f. A(x) satisfies A(x) = (1 + x*A(x)^(p/r))^r, where p=7, r=4.

G.f.: B(x)^4, where B(x) is the g.f. of A002296.