A022198 Gaussian binomial coefficients [ n,7 ] for q = 3.

1, 3280, 8069620, 18326727760, 40581331447162, 89117945389585840, 195168545232713290660, 427028776969176679964080, 934054234760012359481199283, 2042880353039758115797506899680, 4467854961017673003571751798888920

Offset: 7

Author

N. J. A. Sloane, Jun 14 1998

Keywords

• nonn
• easy

References

• F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 7..200

Programs

Magma

r:=7; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016

Mathematica

Table[QBinomial[n, 7, 3], {n, 7, 20}] (* Vincenzo Librandi, Aug 07 2016 *)

PARI

r=7; q=3; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, May 30 2018

Sage

[gaussian_binomial(n,7,3) for n in range(7,18)] # Zerinvary Lajos, May 25 2009

Formula

G.f.: x^7/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)*(1-2187*x)). - Vincenzo Librandi, Aug 07 2016

a(n) = Product_{i=1..7} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 07 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 07 2016