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Search: id:A006110
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| A006110 |
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Gaussian binomial coefficient [ n,5 ] for q=2.
(Formerly M5327)
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+0
1
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| 1, 63, 2667, 97155, 3309747, 109221651, 3548836819, 114429029715, 3675639930963, 117843461817939, 3774561792168531, 120843139740969555, 3867895279362300499
(list; graph; listen)
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OFFSET
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5,2
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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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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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a(n)=(1024*32^n-1984*16^n+1240*8^n-310*4^n+31*2^n-1)/9765 - Jim Buddenhagen (jbuddenh(AT)gmail.com), Dec 14 2003
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MAPLE
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seq((1024*32^n-1984*16^n+1240*8^n-310*4^n+31*2^n-1)/9765, n=1..20);
A006110:=1/(z-1)/(4*z-1)/(2*z-1)/(8*z-1)/(16*z-1)/(32*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(Other) sage: [gaussian_binomial(n, 5, 2) for n in xrange(5, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]
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CROSSREFS
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Sequence in context: A075516 A004376 A094938 this_sequence A132051 A069381 A051589
Adjacent sequences: A006107 A006108 A006109 this_sequence A006111 A006112 A006113
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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