A022206 Gaussian binomial coefficients [ n,7 ] for q = 4.

1, 21845, 381767589, 6354157930725, 104514759495347685, 1714043588198181437925, 28089747579101385828291045, 460250514083576206796548772325, 7540859480106603961931048583270885, 123549912998815788062283863044996567525

Offset

7,2

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

Links

Vincenzo Librandi, Table of n, a(n) for n = 7..200

Formula

G.f.: x^7/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..7} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

Mathematica

Table[QBinomial[n, 7, 4], {n, 7, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

Prog

(Sage) [gaussian_binomial(n, 7, 4) for n in range(7, 17)] # Zerinvary Lajos, May 27 2009
(Magma) r:=7; 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=7; q=4; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 04 2018

Crossrefs

Sequence in context: A092006 A034623 A069312 * A251510 A083626 A234214

Adjacent sequences: A022203 A022204 A022205 * A022207 A022208 A022209

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 11 2016

Status

approved