|
|
A006113
|
|
Gaussian binomial coefficient [ n,4 ] for q = 5.
(Formerly M5479)
|
|
1
|
|
|
1, 781, 508431, 320327931, 200525284806, 125368356709806, 78360229974772306, 48975769621072897306, 30609934249224268600431, 19131218685276848401412931, 11957012900737114492991256681, 7473133215765585192791624069181, 4670708278954101902438990598678556
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
4,2
|
|
REFERENCES
|
J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x^4/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..4} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 06 2016
|
|
MAPLE
|
qBinom := proc(n, m, q)
mul( (1-q^(n-i))/(1-q^(i+1)), i=0..m-1) ;
end proc:
qBinom(n, 4, 5) ;
end proc:
|
|
MATHEMATICA
|
|
|
PROG
|
(Sage) [gaussian_binomial(n, 4, 5) for n in range(4, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|