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A022207 Gaussian binomial coefficients [ n,8 ] for q = 4. 1
1, 87381, 6108368805, 406672215935205, 26756185103024942565, 1755207390500040817377765, 115057361291389776393497498085, 7540859480106603961931048583270885, 494205307747746503853075131001823990245 (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..200

FORMULA

G.f.: x^8/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)*(1-65536*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..8} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

MATHEMATICA

QBinomial[Range[8, 20], 8, 4] (* Harvey P. Dale, Jan 27 2012 *)

Table[QBinomial[n, 8, 4], {n, 8, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

PROG

(Sage) [gaussian_binomial(n, 8, 4) for n in xrange(8, 17)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=8; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 11 2016

(PARI) r=8; q=4; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 04 2018

CROSSREFS

Sequence in context: A230489 A098186 A069313 * A251907 A238052 A118899

Adjacent sequences:  A022204 A022205 A022206 * A022208 A022209 A022210

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed by Vincenzo Librandi, Aug 11 2016

STATUS

approved

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Last modified March 19 00:13 EDT 2019. Contains 321306 sequences. (Running on oeis4.)