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A022207
Gaussian binomial coefficients [ n,8 ] for q = 4.
1
1, 87381, 6108368805, 406672215935205, 26756185103024942565, 1755207390500040817377765, 115057361291389776393497498085, 7540859480106603961931048583270885, 494205307747746503853075131001823990245
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
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 range(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: A372277 A098186 A069313 * A251907 A238052 A118899
KEYWORD
nonn,easy
EXTENSIONS
Offset changed by Vincenzo Librandi, Aug 11 2016
STATUS
approved