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A006107 Gaussian binomial coefficient [ n,4 ] for q = 4.

%I A006107 M5445 #28 Sep 08 2022 08:44:34
%S A006107 1,341,93093,24208613,6221613541,1594283908581,408235958349285,
%T A006107 104514759495347685,26756185103024942565,6849609413493939400165,
%U A006107 1753501675591663698472421,448896535558672700374937061,114917519925881846404167134693
%N A006107 Gaussian binomial coefficient [ n,4 ] for q = 4.
%D A006107 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.
%D A006107 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A006107 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A006107 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A006107 Vincenzo Librandi, <a href="/A006107/b006107.txt">Table of n, a(n) for n = 4..200</a>
%H A006107 M. Sved, <a href="/A006095/a006095.pdf">Gaussians and binomials</a>, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
%F A006107 G.f.: x^4/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)). - _Vincenzo Librandi_, Aug 07 2016
%F A006107 a(n) = Product_{i=1..4} (4^(n-i+1)-1)/(4^i-1), by definition. - _Vincenzo Librandi_, Aug 07 2016
%F A006107 a(n) = (4^n-64)*(4^n-16)*(4^n-4)*(4^n-1)/2961100800. - _Robert Israel_, Feb 01 2018
%p A006107 seq((4^n-64)*(4^n-16)*(4^n-4)*(4^n-1)/2961100800, n=4..30); # _Robert Israel_, Feb 01 2018
%t A006107 Table[QBinomial[n, 4, 4], {n, 4, 20}] (* _Vincenzo Librandi_, Aug 07 2016 *)
%o A006107 (Sage) [gaussian_binomial(n,4,4) for n in range(4,14)] # _Zerinvary Lajos_, May 27 2009
%o A006107 (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
%K A006107 nonn,easy
%O A006107 4,2
%A A006107 _N. J. A. Sloane_