This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002301 M1861 N0737 #52 Aug 23 2018 10:26:38 %S A002301 2,8,40,240,1680,13440,120960,1209600,13305600,159667200,2075673600, %T A002301 29059430400,435891456000,6974263296000,118562476032000, %U A002301 2134124568576000,40548366802944000,810967336058880000,17030314057236480000,374666909259202560000 %N A002301 a(n) = n! / 3. %C A002301 a(n) is the number of n-permutations having 1, 2 and 3 in the same cycle. - _Geoffrey Critzer_, Apr 26 2009 %C A002301 a(n) is the total number of 3-cycles in all n-permutations. - _N. J. A. Sloane_, Jul 22 2009 %C A002301 a(n+1) is the number of local maxima summed over all partitions of length n where n>1. - _Michael Somos_, Jul 19 2012 %C A002301 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 %D A002301 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A002301 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A002301 Letterio Toscano, Sulla Derivata di Ordinen della Funzione tg(x), Tohoku Math. J., 42 (1936), 144-154. %H A002301 N. J. A. Sloane, <a href="/A002301/b002301.txt">Table of n, a(n) for n = 3..30</a> %H A002301 M. A. A., <a href="http://math.hawaii.edu/home/pdf/putnam/2006.pdf">The 67th William Lowell Putnam Mathematical Competition</a> Problem A4. %H A002301 L. Solus, <a href="https://arxiv.org/abs/1807.08223">Local h*-polynomials of some weighted projective spaces</a>, arXiv:1807.08223 [math.CO], 2018. %H A002301 <a href="/index/Di#divseq">Index to divisibility sequences</a> %H A002301 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a> %F A002301 E.g.f. with offset = 0: 2/((1-x)^4). - _Sergei N. Gladkovskii_, Aug 16 2012 %F A002301 E.g.f.: x^3/(3*(1-x)). - _Geoffrey Critzer_, Aug 26 2012 %F A002301 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 %t A002301 f[n_]:=n!/3;Array[f,4!,3] (* _Vladimir Joseph Stephan Orlovsky_, Oct 21 2009 *) %o A002301 (PARI) a(n)=n!/3 \\ _Charles R Greathouse IV_, Jan 12 2012 %K A002301 nonn,easy %O A002301 3,1 %A A002301 _N. J. A. Sloane_