A022242 Gaussian binomial coefficients [ n,2 ] for q = 8.

1, 73, 4745, 304265, 19477641, 1246606473, 79783113865, 5106121684105, 326791806956681, 20914675798619273, 1338539252338766985, 85666512159498155145, 5482656778286418474121, 350890033810959074702473

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..200
• Index entries for linear recurrences with constant coefficients, signature (73, -584, 512).

Programs

Magma

r:=2; q:=8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 05 2016

Mathematica

CoefficientList[Series[1/((1-x)(1-8x)(1-64x)), {x,0,25}],x]  (* Harvey P. Dale, Mar 13 2011 *)
Table[QBinomial[n, 2, 8], {n, 2, 20}] (* Vincenzo Librandi, Aug 05 2016 *)

Sage

[gaussian_binomial(n,2,8) for n in range(2,16)] # Zerinvary Lajos, May 28 2009

Formula

G.f.: x^2/[(1-x)(1-8x)(1-64x)].

a(n) = Product_{i=1..2} (8^(n-i+1)-1)/(8^i-1), by definition. - Vincenzo Librandi, Aug 05 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 05 2016