A022222 Gaussian binomial coefficients [ n,4 ] for q = 6.

1, 1555, 2072815, 2698853335, 3500412775495, 4537117983992551, 5880230843762528935, 7620806375898728694055, 9876570938882852540717095, 12800037205947411879866507815, 16588848493045381066264096333351

Offset

4,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..200

Formula

G.f.: x^4/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..4} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Mathematica

Table[QBinomial[n, 4, 6], {n, 4, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

Prog

(Sage) [gaussian_binomial(n, 4, 6) for n in range(4, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; 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=4; 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

Crossrefs

Sequence in context: A235306 A203501 A229434 * A166606 A252313 A252321

Adjacent sequences: A022219 A022220 A022221 * A022223 A022224 A022225

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016

Status

approved