A022190 Gaussian binomial coefficients [n,7] for q = 2.

1, 255, 43435, 6347715, 866251507, 114429029715, 14877590196755, 1919209135381395, 246614610741341843, 31627961868755063955, 4052305562169692070035, 518946525150879134496915, 66441249531569955747981459

Offset

7,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 7..200

Formula

G.f.: x^7/((1-x)*(1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)*(1-32*x)*(1-64*x)*(1-128*x)). - Vincenzo Librandi, Aug 07 2016

a(n) = Product_{i=1..7} (2^(n-i+1)-1)/(2^i-1), by definition. - Vincenzo Librandi, Aug 02 2016

Mathematica

Table[QBinomial[n, 7, 2], {n, 7, 24}] (* Vincenzo Librandi, Aug 02 2016 *)

Prog

(Sage) [gaussian_binomial(n, 7, 2) for n in range(7, 20)] # Zerinvary Lajos, May 25 2009
(Magma) r:=7; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016
(PARI) r=7; q=2; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, May 30 2018

Crossrefs

Sequence in context: A221970 A177897 A160913 * A267545 A069383 A175824

Adjacent sequences: A022187 A022188 A022189 * A022191 A022192 A022193

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 14 1998

Extensions

Changed offset by Vincenzo Librandi, Aug 02 2016

Status

approved