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A006097
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Gaussian binomial coefficient [ n,4 ] for q=2.
(Formerly M5226)
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3
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1, 31, 651, 11811, 200787, 3309747, 53743987, 866251507, 13910980083, 222984027123, 3571013994483, 57162391576563, 914807651274739, 14638597687734259, 234230965858250739, 3747802679431278579, 59965700687947706355, 959458073589354016755
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,2
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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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=4..204
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (31,-310,1240,-1984,1024).
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FORMULA
| G.f.: x^4/((1-x)*(1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)).
a(n) = (2^n-1)*(2^n-2)*(2^n-4)*(2^n-8)/20160. - Bruno Berselli, Aug 29 2011
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MAPLE
| A006097:=-1/(z-1)/(4*z-1)/(2*z-1)/(8*z-1)/(16*z-1); [S. Plouffe in his 1992 dissertation with offset 0.]
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MATHEMATICA
| faq[n_, q_] = Product[(1-q^(1+k))/(1-q), {k, 0, n-1}];
qbin[n_, m_, q_] = faq[n, q]/(faq[m, q]*faq[n-m, q]);
Table[qbin[n, 4, 2], {n, 4, 21}] (* From Jean-François Alcover, Jul 21 2011 *)
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PROG
| (Sage) [gaussian_binomial(n, 4, 2) for n in xrange(4, 22)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]
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CROSSREFS
| Sequence in context: A024446 A020983 A020981 * A000565 A014930 A196988
Adjacent sequences: A006094 A006095 A006096 * A006098 A006099 A006100
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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