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 A088536 Number of unimodal functions [1..n]->[1..n]. 4
 1, 4, 22, 130, 791, 4900, 30738, 194634, 1241383, 7963384, 51325352, 332095816, 2155894508, 14035149748, 91593941402, 599021799242, 3924954250975, 25760310654100, 169322682857430, 1114452091832130, 7344021912458295, 48448974411575280, 319942093205166840, 2114743632331515480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 FORMULA a(n) = Sum_{k=0..n-1} binomial(2k+n-1,2k). Recurrence: 36*n*(2*n-3)*a(n) = 2*(269*n^2-549*n+235)*a(n-1) - (359*n^2-1062*n+907)*a(n-2) + 6*(3*n-8)*(3*n-7)*a(n-3). - Vaclav Kotesovec, Oct 14 2012 a(n) ~ 27^n/(5*2^(2*n-1)*sqrt(3*Pi*n)). - Vaclav Kotesovec, Oct 14 2012 EXAMPLE From Joerg Arndt, May 10 2013: (Start) The a(3) = 22 unimodal maps [1,2,3]->[1,2,3] are 01:  [ 1 1 1 ] 02:  [ 1 1 2 ] 03:  [ 1 1 3 ] 04:  [ 1 2 1 ] 05:  [ 1 2 2 ] 06:  [ 1 2 3 ] 07:  [ 1 3 1 ] 08:  [ 1 3 2 ] 09:  [ 1 3 3 ] 10:  [ 2 1 1 ] 11:  [ 2 2 1 ] 12:  [ 2 2 2 ] 13:  [ 2 2 3 ] 14:  [ 2 3 1 ] 15:  [ 2 3 2 ] 16:  [ 2 3 3 ] 17:  [ 3 1 1 ] 18:  [ 3 2 1 ] 19:  [ 3 2 2 ] 20:  [ 3 3 1 ] 21:  [ 3 3 2 ] 22:  [ 3 3 3 ] (End) MATHEMATICA Table[Sum[Binomial[2k+n-1, 2k], {k, 0, n-1}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 14 2012 *) PROG (PARI) a(n) = sum(k=0, n-1, binomial(2*k+n-1, 2*k)); \\ Joerg Arndt, May 10 2013 CROSSREFS Main diagonal of A071920. Cf. A225006 (unimodal maps [1..n]->[1..n+1]). Sequence in context: A086682 A261399 A155862 * A066380 A180899 A007195 Adjacent sequences:  A088533 A088534 A088535 * A088537 A088538 A088539 KEYWORD nonn AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 16 2003 EXTENSIONS More terms from David Wasserman, Aug 09 2005 STATUS approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)