A022202 Gaussian binomial coefficients [ n,11 ] for q = 3.

1, 265720, 52955405230, 9741692640081640, 1747282899667791058573, 310804949350361548416923680, 55133793282290501540016988429720, 9771253933538933149312961201158497760, 1731212183148357775944585240618840930624286

Offset: 11

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 = 11..200

Programs

Magma

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

PARI

r=11; 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,11,3) for n in range(11,20)] # Zerinvary Lajos, May 28 2009

Formula

G.f.: x^11/((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)). - Vincenzo Librandi, Aug 11 2016

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

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016