A006107 Gaussian binomial coefficient [ n,4 ] for q = 4. (Formerly M5445)

1, 341, 93093, 24208613, 6221613541, 1594283908581, 408235958349285, 104514759495347685, 26756185103024942565, 6849609413493939400165, 1753501675591663698472421, 448896535558672700374937061, 114917519925881846404167134693

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

Vincenzo Librandi, Table of n, a(n) for n = 4..200

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

Adjacent sequences: A006104 A006105 A006106 * A006108 A006109 A006110

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved