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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 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 xrange(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: A300327 A289305 A317556 * A015371 A163582 A239271 Adjacent sequences:  A006104 A006105 A006106 * A006108 A006109 A006110 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 19 04:18 EDT 2019. Contains 321311 sequences. (Running on oeis4.)