A022260 Gaussian binomial coefficients [ n,9 ] for q = 9.

1, 435848050, 170967170463507055, 66327168553990994916016300, 25700421225173962543056800181928315, 9957038381881749517654238255938525131005050, 3857567937595016308705834953070576178084351138070085

Offset

9,2

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 = 9..120

Formula

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

G.f.: x^9/((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)*(1 - 387420489*x)). - Ilya Gutkovskiy, Aug 04 2016

Mathematica

Drop[QBinomial[Range[20], 9, 9], 8] (* Harvey P. Dale, May 30 2012 *)
Table[QBinomial[n, 9, 9], {n, 9, 20}] (* Vincenzo Librandi, Aug 04 2016 *)

Prog

(Sage) [gaussian_binomial(n, 9, 9) for n in range(9, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; 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: A233477 A117631 A022229 * A209210 A047989 A342857

Adjacent sequences: A022257 A022258 A022259 * A022261 A022262 A022263

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

One additional term from Harvey P. Dale, May 30 2012

Status

approved