A022225 Gaussian binomial coefficients [ n,7 ] for q = 6.

1, 335923, 96723701071, 27202382491194295, 7620806375898728694055, 2133612436978999661759040967, 597287733061433620469903134280071, 167202936130018543413483273700960235527, 46806148995565935663430369990805328306755335

Offset

7,2

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 = 7..190

Formula

G.f.: x^7/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)*(1-7776*x)*(1-46656*x)*(1-279936*x)). - Vincenzo Librandi, Aug 12 2016

a(n) = Product_{i=1..7} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 12 2016

Mathematica

Drop[QBinomial[Range[20], 7, 6], 6] (* Harvey P. Dale, Mar 27 2012 *)
Table[QBinomial[n, 7, 6], {n, 7, 20}] (* Vincenzo Librandi, Aug 12 2016 *)

Prog

(Sage) [gaussian_binomial(n, 7, 6) for n in range(7, 16)] # Zerinvary Lajos, May 27 2009
(Magma) r:=7; 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=7; 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: A346028 A268280 A234081 * A114674 A185475 A224632

Adjacent sequences: A022222 A022223 A022224 * A022226 A022227 A022228

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved