A022229 Gaussian binomial coefficients [ n,11 ] for q = 6.

1, 435356467, 162458788655384143, 59213707780769522731688119, 21499147706200521642647791579711015, 7800830687562794744818371174867996113478343

Offset

11,2

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 = 11..130

Index entries for Gaussian binomial coefficients

Formula

a(n) ~ k*362797056^n for a constant k. - Charles R Greathouse IV, Oct 14 2014

G.f.: x^11/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)*(1-7776*x)*(1-46656*x)*(1-279936*x)*(1-1679616*x)*(1-10077696*x)*(1-60466176*x)*(1-362797056*x)). - Vincenzo Librandi, Aug 12 2016

a(n) = Product_{i=1..11} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 12 2016

Maple

seq(eval(expand(QDifferenceEquations:-QBinomial(n, 11, q)), q=6), n=11..20); # Robert Israel, Oct 14 2014

Mathematica

QBinomial[Range[11, 20], 11, 6] (* Harvey P. Dale, Oct 06 2014 *)

Prog

(SageMath) [gaussian_binomial(n, 11, 6) for n in range(11, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Oct 14 2014
(PARI) a(n)=prod(i=1, 11, (6^(n-i+1)-1)/(6^i-1)) \\ Charles R Greathouse IV, Oct 14 2014

Crossrefs

Sequence in context: A283872 A233477 A117631 * A022260 A209210 A047989

Adjacent sequences: A022226 A022227 A022228 * A022230 A022231 A022232

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved