A022259 Gaussian binomial coefficients [ n,8 ] for q = 9.

1, 48427561, 2110705802810605, 90983770072735012966405, 3917150001348391097251303957615, 168623318873839155489174680568370759015, 7258694620170400715835032365617891585605600635, 312463067466939934510699888848526630609825159414503235

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..140

Formula

a(n) = Product_{i=1..8} (9^(n-i+1)-1)/(9^i-1), by definition. - Vincenzo Librandi, Aug 04 2016

G.f.: x^8/((1 - x)*(1 - 9*x)*(1 - 81*x)*(1 - 729*x)*(1 - 6561*x)*(1 - 59049*x)*(1 - 531441*x)*(1 - 4782969*x)*(1 - 43046721*x)). - Ilya Gutkovskiy, Aug 04 2016

Mathematica

QBinomial[Range[8, 20], 8, 9] (* Harvey P. Dale, Jun 21 2012 *)
Table[QBinomial[n, 8, 9], {n, 8, 20}] (* Vincenzo Librandi, Aug 04 2016 *)

Prog

(Sage) [gaussian_binomial(n, 8, 9) for n in range(8, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 04 2016

Crossrefs

Sequence in context: A121491 A300568 A210334 * A290501 A016823 A016859

Adjacent sequences: A022256 A022257 A022258 * A022260 A022261 A022262

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Offset corrected by Harvey P. Dale, Jun 21 2012

Status

approved