A295446 a(n) = (10*n)!*(6*n)!/((9*n)!*(5*n)!*(2*n)!).

1, 30, 2090, 165648, 13873002, 1198158780, 105534616880, 9423350114880, 849915927124330, 77248168052615490, 7063878565972568340, 649143744147709730400, 59897782807583055382320, 5545885349166413944400400, 514993443497655350848314048, 47943397954241622806694753648

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

G.f.: hypergeom([1/10, 1/6, 3/10, 1/2, 7/10, 5/6, 9/10], [1/9, 2/9, 4/9, 5/9, 7/9, 8/9], 51200000/531441*x).

a(n) = binomial(10*n,n)*binomial(6*n,n)/binomial(2*n,n) = binomial(10*n,n)*binomial(7*n,2*n)/binomial(7*n,n). - Chai Wah Wu, Feb 15 2026

a(n) ~ 2^(14*n) * 5^(5*n) / (3^(12*n+1/2) * sqrt(Pi*n)). - Amiram Eldar, Feb 23 2026

Mathematica

a[n_] := (10*n)!*(6*n)!/((9*n)!*(5*n)!*(2*n)!); Array[a, 16, 0] (* Amiram Eldar, Feb 23 2026 *)

Prog

(Python)
from math import comb
def A295446(n): return comb(10*n, n)*comb(6*n, n)//comb(2*n, n) # Chai Wah Wu, Feb 15 2026

Crossrefs

Cf. A295431.

Sequence in context: A330598 A255958 A092617 * A056093 A056070 A301377

Adjacent sequences: A295443 A295444 A295445 * A295447 A295448 A295449

Keyword

nonn,easy

Author

Gheorghe Coserea, Nov 27 2017

Status

approved