A022203 Gaussian binomial coefficients [ n,12 ] for q = 3.

1, 797161, 476599444231, 263026177881648511, 141530177899268957392924, 75525744222315755534269847164, 40192610828533997938427918835113044, 21369772545260475331545384574852469714164, 11358504503408920628447755309084790198295654610

Offset: 12

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 = 12..180

Programs

Magma

r:=12; 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, 12, 3], {n, 12, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

PARI

r=12; q=3; for(n=r,35, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 01 2018

Sage

[gaussian_binomial(n,12,3) for n in range(12,21)] # Zerinvary Lajos, May 28 2009

Formula

G.f.: x^12/((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)*(1-177147*x)*(1-531441*x) ). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..12} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016