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 A002301 a(n) = n! / 3. (Formerly M1861 N0737) 12
 2, 8, 40, 240, 1680, 13440, 120960, 1209600, 13305600, 159667200, 2075673600, 29059430400, 435891456000, 6974263296000, 118562476032000, 2134124568576000, 40548366802944000, 810967336058880000, 17030314057236480000, 374666909259202560000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS 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 REFERENCES 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. LINKS N. J. A. Sloane, Table of n, a(n) for n = 3..30 M. A. A., The 67th William Lowell Putnam Mathematical Competition Problem A4. L. Solus, Local h*-polynomials of some weighted projective spaces, arXiv:1807.08223 [math.CO], 2018. FORMULA E.g.f. with offset = 0: 2/((1-x)^4). - Sergei N. Gladkovskii, Aug 16 2012 E.g.f.: x^3/(3*(1-x)). - Geoffrey Critzer, Aug 26 2012 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 MATHEMATICA f[n_]:=n!/3; Array[f, 4!, 3] (* Vladimir Joseph Stephan Orlovsky, Oct 21 2009 *) PROG (PARI) a(n)=n!/3 \\ Charles R Greathouse IV, Jan 12 2012 CROSSREFS Sequence in context: A305406 A296050 A055882 * A319949 A304070 A259869 Adjacent sequences:  A002298 A002299 A002300 * A002302 A002303 A002304 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified August 19 04:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)