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

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

Offset

2,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..200

Index entries for linear recurrences with constant coefficients, signature (73, -584, 512).

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

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 *)

Prog

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

Crossrefs

Sequence in context: A221826 A093273 A183540 * A015260 A089788 A292013

Adjacent sequences: A022239 A022240 A022241 * A022243 A022244 A022245

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Offset changed by Vincenzo Librandi, Aug 05 2016

Status

approved