A295453 a(n) = (15*n)!*n!/((9*n)!*(5*n)!*(2*n)!).

1, 15015, 951425475, 70008087393552, 5472752419793774115, 442152818018970753425640, 36471466447057357977530250960, 3051670756860336385013412647728800, 258020271506436677733823067896257122595, 21990039069051148065537923218288162358113800

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], [1/9, 2/9, 4/9, 1/2, 5/9, 7/9, 8/9], 9765625/108*x).

a(n) = binomial(15*n,6*n)*binomial(6*n,n)/binomial(2*n,n). - Chai Wah Wu, Feb 15 2026

a(n) ~ 5^(10*n) / (2^(2*n+1) * 3^(3*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 22 2026

Mathematica

a[n_] := (15*n)!*n!/((9*n)!*(5*n)!*(2*n)!); Array[a, 10, 0] (* Amiram Eldar, Feb 22 2026 *)

Prog

(Python)
from math import comb
def A295453(n): return comb(15*n, 6*n)*comb(6*n, n)//comb(2*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A200090 A147578 A285993 * A205022 A207297 A151595

Adjacent sequences: A295450 A295451 A295452 * A295454 A295455 A295456

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 27 2017

Status

approved