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A002301
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a(n) = n! / 3.
(Formerly M1861 N0737)
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13
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2, 8, 40, 240, 1680, 13440, 120960, 1209600, 13305600, 159667200, 2075673600, 29059430400, 435891456000, 6974263296000, 118562476032000, 2134124568576000, 40548366802944000, 810967336058880000, 17030314057236480000, 374666909259202560000
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OFFSET
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3,1
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COMMENTS
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a(n) is the number of n-permutations having 1, 2 and 3 in the same cycle. - Geoffrey Critzer, Apr 26 2009
a(n) is the total number of 3-cycles in all n-permutations. - N. J. A. Sloane, Jul 22 2009
a(n+1) is the number of local maxima summed over all partitions of length n where n>1. - Michael Somos, Jul 19 2012
For n>2, n!/3 is the number of lattice points in the open parallelepiped of the factoradic n-simplex. See Remark 3.1 in the article by L. Solus below. - Liam Solus, Aug 23 2018
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Letterio Toscano, Sulla Derivata di Ordinen della Funzione tg(x), Tohoku Math. J., 42 (1936), 144-154.
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LINKS
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FORMULA
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G.f. 2 + 8*x/(G(0)-4*x) where G(k) = x*(k+4) + 1 - x*(k+5)/G(k+1); (continued fraction, Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Aug 15 2012
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MATHEMATICA
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PROG
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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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STATUS
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approved
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