A022204 Gaussian binomial coefficients [ n,5 ] for q = 4.

1, 1365, 1490853, 1550842085, 1594283908581, 1634141006295525, 1673768626404966885, 1714043588198181437925, 1755207390500040817377765, 1797339217481455290934231525, 1840477112202685809580351554021

Offset

5,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 5..200

Formula

G.f.: x^5/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..5} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Mathematica

Table[QBinomial[n, 5, 4], {n, 5, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

Prog

(Sage) [gaussian_binomial(n, 5, 4) for n in range(5, 16)] # Zerinvary Lajos, May 27 2009
(Magma) r:=5; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 11 2016
(PARI) r=5; q=4; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 01 2018

Crossrefs

Sequence in context: A069310 A096117 A140936 * A015405 A295466 A292780

Adjacent sequences: A022201 A022202 A022203 * A022205 A022206 A022207

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016

Status

approved