A022196 Gaussian binomial coefficients [ n,5 ] for q = 3.

1, 364, 99463, 25095280, 6174066262, 1506472167928, 366573514642546, 89117945389585840, 21658948312410865183, 5263390747480701708292, 1279025522911365763892449, 310804949350361548416923680, 75525744222315755534269847164

Offset: 5

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 5..200

Programs

Magma

r:=5; 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, 5, 3], {n, 5, 20}] (* Vincenzo Librandi, Aug 07 2016 *)

PARI

r=5; 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,5,3) for n in range(5,17)] # Zerinvary Lajos, May 25 2009

Formula

G.f.: x^5/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)). - Vincenzo Librandi, Aug 07 2016

a(n) = Product_{i=1..5} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 07 2016