A295455 a(n) = (15*n)!*(4*n)!/((12*n)!*(5*n)!*(2*n)!).

1, 273, 197925, 163599348, 142968550725, 128870282292648, 118480953427211364, 110433519432700272900, 103975323964183657238085, 98653477096436613397662000, 94177063016288953736433769800, 90349590539197254060291386954952, 87032952761243666079438661028681700

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], 263671875/262144*x).

a(n) = binomial(15*n,3*n)*binomial(4*n,2*n)/binomial(5*n,2*n). - Chai Wah Wu, Feb 15 2026

a(n) ~ 3^(3*n) * 5^(10*n) / (2^(18*n+1) * sqrt(Pi*n)). - Amiram Eldar, Feb 22 2026

Mathematica

a[n_] := (15*n)!*(4*n)!/((12*n)!*(5*n)!*(2*n)!); Array[a, 13, 0] (* Amiram Eldar, Feb 22 2026 *)

Prog

(Python)
from math import comb
def A295455(n): return comb(15*n, 3*n)*comb(4*n, 2*n)//comb(5*n, 2*n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A321035 A225702 A307537 * A174771 A031417 A361797

Adjacent sequences: A295452 A295453 A295454 * A295456 A295457 A295458

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 27 2017

Status

approved