A022226 Gaussian binomial coefficients [ n,8 ] for q = 6.

1, 2015539, 3482055254095, 5875718100153221815, 9876570938882852540717095, 16590980186519640252690843276487, 27867073064694433516284053323814269063, 46806148995565935663430369990805328306755335, 78616403557485470161203927752846473114607475506695

Offset

8,2

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 = 8..170

Formula

G.f.: -x^8/((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)). - Harvey P. Dale, Jun 24 2011

a(n) = Product_{i=1..8} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 12 2016

Mathematica

QBinomial[Range[8, 20], 8, 6] (* Harvey P. Dale, Jun 24 2011 *)
Table[QBinomial[n, 8, 6], {n, 8, 20}] (* Vincenzo Librandi, Aug 12 2016 *)

Prog

(Sage) [gaussian_binomial(n, 8, 6) for n in range(8, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; 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=8; 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: A233996 A359534 A081398 * A345086 A345085 A032754

Adjacent sequences: A022223 A022224 A022225 * A022227 A022228 A022229

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Harvey P. Dale, Jun 24 2011

Offset changed by Vincenzo Librandi, Aug 12 2016

Status

approved