A022200 Gaussian binomial coefficients [ n,9 ] for q = 3.

1, 29524, 653757313, 13362799477720, 266307564861468823, 5263390747480701708292, 103741619611085612124067759, 2042880353039758115797506899680, 40216143252770054194345243936096486, 791614563787525746761491781638123230424

Offset: 9

Author

N. J. A. Sloane

Keywords

• nonn

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 = 9..200

Programs

Magma

r:=9; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 10 2016

Mathematica

Table[QBinomial[n, 9, 3], {n, 9, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

PARI

r=9; 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,9,3) for n in range(9,19)] # Zerinvary Lajos, May 25 2009

Formula

G.f.: x^9/((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)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..9} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 10 2016