A022228 Gaussian binomial coefficients [ n,10 ] for q = 6.

1, 72559411, 4512744117222991, 274137535269957102205111, 16588848493045381066264096333351, 1003193244092547201468344847250540706503, 60660559425600837230512947639888522210296616583, 3667925165214264518763232198536887427772300866095529223

Offset

10,2

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 = 10..140

Formula

G.f.: x^10/((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)). - Vincenzo Librandi, Aug 12 2016

a(n) = Product_{i=1..10} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 12 2016

Mathematica

Table[QBinomial[n, 10, 6], {n, 10, 20}] (* Vincenzo Librandi, Aug 12 2016 *)

Prog

(Sage) [gaussian_binomial(n, 10, 6) for n in range(10, 18)] # Zerinvary Lajos, May 27 2009
(Magma) r:=10; 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=10; 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: A104942 A104849 A138058 * A032431 A186535 A244924

Adjacent sequences: A022225 A022226 A022227 * A022229 A022230 A022231

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 12 2016

Status

approved