A295452 a(n) = (10*n)!*(6*n)!*n!/((7*n)!*(5*n)!*(3*n)!*(2*n)!).

1, 360, 426360, 583731720, 848084358264, 1272844124730360, 1949962324582133400, 3029870085304407766200, 4756833647064253405342840, 7527387071973766687474317120, 11986073514194153892621775416360, 19182204664545386655937834503826320, 30826701085749480283253960554248940440

Offset

0,2

Links

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

Formula

G.f.: hypergeom([1/10, 1/6, 3/10, 1/2, 7/10, 5/6, 9/10], [1/7, 2/7, 3/7, 4/7, 5/7, 6/7], 1382400000/823543*x).

a(n) = binomial(10*n,3*n)*binomial(6*n,n)/binomial(2*n,n). - Chai Wah Wu, Feb 15 2026

a(n) ~ 2^(14*n) * 3^(3*n) * 5^(5*n) / (7^(7*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 22 2026

Mathematica

a[n_] := (10*n)!*(6*n)!*n!/((7*n)!*(5*n)!*(3*n)!*(2*n)!); Array[a, 13, 0] (* Amiram Eldar, Feb 22 2026 *)

Prog

(Python)
from math import comb
def A295452(n): return comb(10*n, 3*n)*comb(6*n, n)//comb(2*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A317796 A145412 A156032 * A330906 A003799 A003930

Adjacent sequences: A295449 A295450 A295451 * A295453 A295454 A295455

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 27 2017

Status

approved