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A032261
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Number of bracelets with n labeled beads of 3 colors.
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1
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1, 3, 9, 27, 243, 2916, 43740, 787320, 16533720, 396809280, 10713850560, 321415516800, 10606712054400, 381841633958400, 14891823724377600, 625456596423859200, 28145546839073664000, 1350986248275535872000
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OFFSET
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0,2
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LINKS
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FORMULA
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"DIJ" (bracelet, indistinct, labeled) transform of 3, 0, 0, 0, ...
a(n) = 3^n*(n-1)!/2 for n >= 3.
E.g.f.: 1 + (g(x) + g(x)^2/2 - log(1-g(x)))/2 where g(x) = 3*x. - Andrew Howroyd, Sep 12 2018
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PROG
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(PARI) seq(n)={my(p=3*x + O(x*x^n)); Vec(1 + serlaplace(p + p^2/2 - log(1-p))/2)} \\ Andrew Howroyd, Sep 12 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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