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A022226 Gaussian binomial coefficients [ n,8 ] for q = 6. 1
1, 2015539, 3482055254095, 5875718100153221815, 9876570938882852540717095, 16590980186519640252690843276487, 27867073064694433516284053323814269063, 46806148995565935663430369990805328306755335, 78616403557485470161203927752846473114607475506695 (list; graph; refs; listen; history; text; internal format)
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 xrange(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: A172791 A233996 A081398 * A032754 A271768 A104441

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

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Last modified March 22 12:38 EDT 2019. Contains 321421 sequences. (Running on oeis4.)