A295448 a(n) = (18*n)!*(3*n)!*(2*n)!/((9*n)!*(7*n)!*(6*n)!*n!).

1, 58344, 12021607800, 2822244125414280, 700261879438261335160, 179189518952510712859732344, 46764098183514722386761235104408, 12372233944479031609487359517835891000, 3306338458421450496220314582388757069245560, 890410398621683112497449813467376431287399918400

Offset

0,2

Links

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

Formula

G.f.: hypergeom([1/18, 5/18, 7/18, 1/2, 11/18, 13/18, 17/18], [1/7, 2/7, 3/7, 4/7, 5/7, 6/7], 235092492288/823543*x).

a(n) = binomial(18*n,9*n)*binomial(9*n,2*n)*binomial(2*n,n)/(binomial(6*n,3*n)*binomial(3*n,n)). - Chai Wah Wu, Feb 15 2026

a(n) ~ 2^(14*n) * 3^(15*n) / (7^(7*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 23 2026

Mathematica

a[n_] := (18*n)!*(3*n)!*(2*n)!/((9*n)!*(7*n)!*(6*n)!*n!); Array[a, 10, 0] (* Amiram Eldar, Feb 23 2026 *)

Prog

(Python)
from math import comb
def A295448(n): return comb(18*n, 9*n)*comb(9*n, 2*n)*comb(2*n, n)//(comb(6*n, 3*n)*comb(3*n, n)) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A237402 A210106 A227496 * A220987 A273318 A230576

Adjacent sequences: A295445 A295446 A295447 * A295449 A295450 A295451

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 27 2017

Status

approved