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

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

Offset

3,2

Links

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

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

Mathematica

Table[QBinomial[n, 3, 6], {n, 3, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

Prog

(Sage) [gaussian_binomial(n, 3, 6) for n in range(3, 16)] # Zerinvary Lajos, May 27 2009
(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
(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
(GAP) List([3..15], n->Product([1..3], i->(6^(n-i+1)-1)/(6^i-1))); # Muniru A Asiru, Jul 04 2018

Crossrefs

Sequence in context: A322882 A256594 A229433 * A121918 A097735 A063485

Adjacent sequences: A022218 A022219 A022220 * A022222 A022223 A022224

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016

Status

approved