A022237 Gaussian binomial coefficients [ n,8 ] for q = 7.

1, 6725601, 39579496050501, 228835075951868449701, 1319738336534843578720956303, 7608481579300344488889504665693103, 43861755035533826577243997768793428552803, 252854596323205247053675081227392663237129990403

Offset

8,2

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 = 8..150

Formula

a(n) = Product_{i=1..8} (7^(n-i+1)-1)/(7^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

G.f.: x^8/((1 - x)*(1 - 7*x)*(1 - 49*x)*(1 - 343*x)*(1 - 2401*x)*(1 - 16807*x)*(1 - 117649*x)*(1 - 823543*x)*(1 - 5764801*x)). - Ilya Gutkovskiy, Aug 06 2016

Mathematica

Drop[QBinomial[Range[0, 20], 8, 7], 8] (* Harvey P. Dale, Mar 26 2013 *)

Prog

(Sage) [gaussian_binomial(n, 8, 7) for n in range(8, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016

Crossrefs

Sequence in context: A266914 A234711 A309385 * A273753 A116173 A345608

Adjacent sequences: A022234 A022235 A022236 * A022238 A022239 A022240

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

One additional term, offset corrected, Harvey P. Dale, Mar 26 2013

Status

approved