A022201 Gaussian binomial coefficients [ n,10 ] for q = 3.

1, 88573, 5883904390, 360801469802830, 21571273555248777493, 1279025522911365763892449, 75628919722004322604209288760, 4467854961017673003571751798888920, 263862583736385343242102717216527933566

Offset: 10

Author

N. J. A. Sloane

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 = 10..200

Programs

Magma

r:=10; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 11 2016

Mathematica

Table[QBinomial[n, 10, 3], {n, 10, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

PARI

r=10; q=3; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 01 2018

Sage

[gaussian_binomial(n,10,3) for n in range(10,19)] # Zerinvary Lajos, May 25 2009

Formula

G:f.: x^10/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)*(1-2187*x)*(1-6561*x)*(1-19683*x)*(1-59049*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..10} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016