A295467 a(n) = (15*n)!*n!/((8*n)!*(5*n)!*(3*n)!).

1, 45045, 9704539845, 2437781614596900, 651257537955459119685, 179888173423256639605246920, 50740927694468549286238961648100, 14520123213959375344187178875204676660, 4199008318481460680983513774150641241683525, 1224055446916973458193847787407419946733555964400

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Formula

G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8], 5189853515625/16777216*x).

a(n) = binomial(15*n,7*n)*binomial(7*n,2*n)/binomial(3*n,n) = binomial(15*n,7*n)*binomial(8*n,3*n)/binomial(8*n,n). - Chai Wah Wu, Feb 16 2026

a(n) ~ 3^(12*n) * 5^(10*n) / (2^(24*n+2) * sqrt(Pi*n)). - Amiram Eldar, Feb 21 2026

Mathematica

a[n_] := (15*n)!*n!/((8*n)!*(5*n)!*(3*n)!); Array[a, 10, 0] (* Amiram Eldar, Feb 21 2026 *)

Prog

(Python)
from math import comb
def A295467(n): return comb(15*n, 7*n)*comb(7*n, 2*n)//comb(3*n, n) # Chai Wah Wu, Feb 16 2026

Crossrefs

Cf. A295431.

Sequence in context: A230618 A185574 A209783 * A158931 A162894 A031851

Adjacent sequences: A295464 A295465 A295466 * A295468 A295469 A295470

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 28 2017

Status

approved