A114253 a(n) = C(5+2*n,5+n)*C(10+2*n,0+n).

1, 84, 3276, 92400, 2187900, 46558512, 923410488, 17439488352, 317907339750, 5644249611000, 98209943231400, 1682207622669600, 28457345616827400, 476607460678020000, 7917519856977720000, 130649634333275016960, 2143941655711783421340, 35018537985874435552560

Offset: 0

Author

Zerinvary Lajos, Feb 04 2006

Keywords

• easy
• nonn
• changed

Examples

			If n=1 then C(5+2*1,5+1)*C(10+2*1,0+1) = C(7,6)*C(12,1) = 7*12 = 84.
If n=11 then C(5+2*n,5+n)*C(10+2*n,0+n) = C(27,16)*C(32,11) = 13037895*129024480 = 1682207622669600.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..828

Crossrefs

Cf. A003516, A004311, A062190.

Programs

Maple

seq(binomial(5+2*n,5+n)*binomial(10+2*n,n),n=0..30); # Robert Israel, Jan 11 2019

Mathematica

a[n_] := Binomial[2*n + 5, n + 5]*Binomial[2*n + 10, n]; Array[a, 20, 0] (* Amiram Eldar, Sep 06 2025 *)

Formula

From Robert Israel, Jan 11 2019: (Start)

(n+1)^2*(11+n)*a(n+1) = 4*(7+2*n)*(3+n)*(11+2*n)*a(n).

a(n) ~ 32768*16^n/(Pi*n). (End)

a(n) = A003516(n+2) * A004311(n+5). - Amiram Eldar, Sep 06 2025