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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 May 22 21:40 EDT 2017. Contains 286906 sequences.