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Search: id:A006097
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| A006097 |
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Gaussian binomial coefficient [ n,4 ] for q=2.
(Formerly M5226)
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+0
2
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| 1, 31, 651, 11811, 200787, 3309747, 53743987, 866251507, 13910980083, 222984027123, 3571013994483, 57162391576563, 914807651274739, 14638597687734259, 234230965858250739, 3747802679431278579, 59965700687947706355, 959458073589354016755
(list; graph; listen)
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OFFSET
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4,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
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LINKS
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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.
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FORMULA
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G.f.: x^4/((1-x)(1-2x)(1-4x)(1-8x)(1-16x)).
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MAPLE
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A006097:=-1/(z-1)/(4*z-1)/(2*z-1)/(8*z-1)/(16*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(Other) 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
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Sequence in context: A024446 A020983 A020981 this_sequence A000565 A014930 A061252
Adjacent sequences: A006094 A006095 A006096 this_sequence A006098 A006099 A006100
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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