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A006107 Gaussian binomial coefficient [ n,4 ] for q = 4.
(Formerly M5445)
1
1, 341, 93093, 24208613, 6221613541, 1594283908581, 408235958349285, 104514759495347685, 26756185103024942565, 6849609413493939400165, 1753501675591663698472421, 448896535558672700374937061, 114917519925881846404167134693 (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
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
FORMULA
G.f.: x^4/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..4} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 07 2016
a(n) = (4^n-64)*(4^n-16)*(4^n-4)*(4^n-1)/2961100800. - Robert Israel, Feb 01 2018
MAPLE
seq((4^n-64)*(4^n-16)*(4^n-4)*(4^n-1)/2961100800, n=4..30); # Robert Israel, Feb 01 2018
MATHEMATICA
Table[QBinomial[n, 4, 4], {n, 4, 20}] (* Vincenzo Librandi, Aug 07 2016 *)
PROG
(Sage) [gaussian_binomial(n, 4, 4) for n in range(4, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016
CROSSREFS
Sequence in context: A289305 A309285 A317556 * A015371 A328665 A163582
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 14 12:23 EDT 2024. Contains 371661 sequences. (Running on oeis4.)