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, 42074892286587392832600

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Wikipedia, Fuss-Catalan number.

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.

a(n) ~ 7^(7*n+7/2) / (8^(2*n+1) * 3^(6*n+9/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 22 2025

Mathematica

a[n_] := 4 * Binomial[7*n+4, n] / (7*n+4); Array[a, 20, 0] (* Amiram Eldar, Sep 22 2025 *)

Prog

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

Crossrefs

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

Cf. A002296, A386380.

Sequence in context: A386667 A199752 A264607 * A307941 A084973 A379282

Adjacent sequences: A386389 A386390 A386391 * A386393 A386394 A386395

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 20 2025

Status

approved