|
|
A022234
|
|
Gaussian binomial coefficients [ n,5 ] for q = 7.
|
|
1
|
|
|
1, 19608, 336416907, 5670690600800, 95347005938577702, 1602592475815614015216, 26935000671139346639437914, 452697105941691435357049202400, 7608481579300344488889504665693103, 127875753071992714335358328311551866824
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
5,2
|
|
REFERENCES
|
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Product_{i=1..5} (7^(n-i+1)-1)/(7^i-1), by definition. - Vincenzo Librandi, Aug 06 2016
G.f.: x^5/((1 - x)*(1 - 7*x)*(1 - 49*x)*(1 - 343*x)*(1 - 2401*x)*(1 - 16807*x)). - Ilya Gutkovskiy, Aug 06 2016
|
|
MATHEMATICA
|
|
|
PROG
|
(Sage) [gaussian_binomial(n, 5, 7) for n in range(5, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=5; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016
(PARI) r=5; q=7; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 13 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|