A022235 Gaussian binomial coefficients [ n,6 ] for q = 7.

1, 137257, 16484565700, 1945063360640100, 228930106321885702602, 26935000671139346639437914, 3168902828959544132129870582100, 372818701621367349292382501162685300, 43861755035533826577243997768793428552803

Offset

6,2

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 = 6..200

Formula

a(n) = Product_{i=1..6} (7^(n-i+1)-1)/(7^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

G.f.: x^6/((1 - x)*(1 - 7*x)*(1 - 49*x)*(1 - 343*x)*(1 - 2401*x)*(1 - 16807*x)*(1 - 117649*x)). - Ilya Gutkovskiy, Aug 06 2016

Mathematica

Table[QBinomial[n, 6, 7], {n, 6, 20}] (* Vincenzo Librandi, Aug 06 2016 *)

Prog

(Sage) [gaussian_binomial(n, 6, 7) for n in range(6, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=6; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016
(PARI) r=6; q=7; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 13 2018

Crossrefs

Sequence in context: A191819 A015071 A130422 * A234225 A110598 A069336

Adjacent sequences: A022232 A022233 A022234 * A022236 A022237 A022238

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 06 2016

Status

approved