A022253 Gaussian binomial coefficients [ n,2 ] for q = 9.

1, 91, 7462, 605242, 49031983, 3971657053, 321704819164, 26058095733124, 2110705802810605, 170967170463507055, 13848340811466703906, 1121715605764106708446, 90858964067210376612667, 7359576089446900104682897

Offset

2,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (91, -819, 729).

Formula

G.f.: 1/[(1-x)(1-9x)(1-81x)].

a(n) = Product_{i=1..2} (9^(n-i+1)-1)/(9^i-1), by definition. - Vincenzo Librandi, Aug 04 2016

Mathematica

Table[QBinomial[n, 2, 9], {n, 2, 20}] (* Vincenzo Librandi, Aug 04 2016 *)

Prog

(Sage) [gaussian_binomial(n, 2, 9) for n in range(2, 16)] # Zerinvary Lajos, May 28 2009
(Magma) r:=2; q:=9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 04 2016

Crossrefs

Sequence in context: A238541 A217853 A210461 * A172174 A060078 A202564

Adjacent sequences: A022250 A022251 A022252 * A022254 A022255 A022256

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Offset changed by Vincenzo Librandi, Aug 04 2016

Status

approved