A022232 Gaussian binomial coefficients [ n,3 ] for q = 7.

1, 400, 140050, 48177200, 16531644851, 5670690600800, 1945063360640100, 667157540444234400, 228835075951868449701, 78490432990886231801200, 26922218610904350161500150, 9234320988196680367732171600

Offset

3,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..200

Formula

G.f.: x^3/((1-x)*(1-7*x)*(1-49*x)*(1-343*x)).

a(n) = Product_{i=1..3} (7^(n-i+1)-1)/(7^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

Mathematica

Table[QBinomial[n, 3, 7], {n, 3, 20}] (* Vincenzo Librandi, Aug 06 2016 *)

Prog

(Sage) [gaussian_binomial(n, 3, 7) for n in range(3, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016
(PARI) r=3; q=7; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 13 2018

Crossrefs

Sequence in context: A231288 A210262 A151608 * A151652 A197441 A268366

Adjacent sequences: A022229 A022230 A022231 * A022233 A022234 A022235

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 06 2016

Status

approved