A022220 Gaussian binomial coefficients [ n,2 ] for q = 6.

1, 43, 1591, 57535, 2072815, 74630671, 2686760143, 96723701071, 3482055254095, 125354001240655, 4512744117222991, 162458788655384143, 5848516394205967951, 210546590207087679055, 7579677247549193442895, 272868380912335185925711

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..200
• Index entries for linear recurrences with constant coefficients, signature (43, -258, 216).

Programs

Magma

r:=2; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 10 2016

Mathematica

Table[QBinomial[n, 2, 6], {n, 2, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

PARI

r=2; 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

Sage

[gaussian_binomial(n,2,6) for n in range(2,17)] # Zerinvary Lajos, May 28 2009

Formula

G.f.: x^2/((1-x)*(1-6*x)*(1-36*x)).

a(n) = Product_{i=1..2} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 16 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 10 2016