A022227 Gaussian binomial coefficients [ n,9 ] for q = 6.

1, 12093235, 125354001240655, 1269155234987097152695, 12800037205947411879866507815, 129011474730413928552335877184470727, 1300166289917858220549677344211755721874055

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..150

Formula

G.f.: x^9/((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)). - Vincenzo Librandi, Aug 12 2016

a(n) = Product_{i=1..9} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 12 2016

Mathematica

Table[QBinomial[n, 9, 6], {n, 9, 20}] (* Vincenzo Librandi, Aug 12 2016 *)

Prog

(Sage) [gaussian_binomial(n, 9, 6) for n in range(9, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 12 2016
(PARI) r=9; q=6; 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: A345718 A346359 A233634 * A206750 A178056 A132291

Adjacent sequences: A022224 A022225 A022226 * A022228 A022229 A022230

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 12 2016

Status

approved