A022221 Gaussian binomial coefficients [ n,3 ] for q = 6.

1, 259, 57535, 12485095, 2698853335, 583026951031, 125936508182839, 27202382491194295, 5875718100153221815, 1269155234987097152695, 274137535269957102205111, 59213707780769522731688119, 12790160886494733304250601655

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..200

Programs

GAP

List([3..15],n->Product([1..3],i->(6^(n-i+1)-1)/(6^i-1))); # Muniru A Asiru, Jul 04 2018

Magma

r:=3; q:=6; [&*[(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, 3, 6], {n, 3, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

PARI

r=3; q=6; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 07 2018

Sage

[gaussian_binomial(n,3,6) for n in range(3,16)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^3/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..3} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016