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 A225006 Number of n X n 0..1 arrays with rows unimodal and columns nondecreasing. 3
 1, 2, 9, 50, 295, 1792, 11088, 69498, 439791, 2803658, 17978389, 115837592, 749321716, 4863369656, 31655226108, 206549749930, 1350638103791, 8848643946550, 58069093513635, 381650672631330, 2511733593767295, 16550500379912640, 109176697072162080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Diagonal of A225010. Number of unimodal maps [1..n]->[1..n+1], see example. - Joerg Arndt, May 10 2013 LINKS G. C. Greubel and R. H. Hardin, Table of n, a(n) for n = 0..1000 (terms 1..51 from R. H. Hardin) FORMULA From Vaclav Kotesovec, May 22 2013: (Start) Empirical: 4*n*(2*n-1)*(5*n-7)*a(n) = 2*(145*n^3 - 343*n^2 + 235*n - 48)*a(n-1) - 3*(3*n-4)*(3*n-2)*(5*n-2)*a(n-2). a(n) ~ 3^(3*n+3/2)/(5*2^(2*n+1)*sqrt(Pi*n)). (End) a(n) = A261668(n)+1. a(n) = Sum_{d=0..n} binomial(2d+n-1,n-1). Also, a(n) is the coefficient of x^(2n) in (1+x)^(-n-1)/(1-x). - Max Alekseyev, Sep 14 2015 EXAMPLE Some solutions for n=3 ..0..1..1....0..1..0....0..0..1....0..0..0....0..0..0....0..0..0....0..0..0 ..1..1..1....0..1..0....1..1..1....0..0..0....0..0..0....0..1..0....0..0..1 ..1..1..1....0..1..1....1..1..1....0..0..1....0..1..0....1..1..1....0..1..1 From Joerg Arndt, May 10 2013: (Start) The a(2) = 9 unimodal maps [1,2]->[1,2,3] are 01:  [ 1 1 ] 02:  [ 1 2 ] 03:  [ 1 3 ] 04:  [ 2 1 ] 05:  [ 2 2 ] 06:  [ 2 3 ] 07:  [ 3 1 ] 08:  [ 3 2 ] 09:  [ 3 3 ] (End) MATHEMATICA a[n_] := Sum[Binomial[2d+n-1, n-1], {d, 0, n}]; Array[a, 30] (* Jean-François Alcover, Feb 17 2016, after Max Alekseyev *) PROG (PARI) { a(n) = polcoeff( (1+x+O(x^(2*n+1)))^(-n-1)/(1-x), 2*n) } CROSSREFS Cf. A088536 (unimodal maps [1..n]->[1..n]). Sequence in context: A055997 A115599 A047069 * A211789 A192945 A271960 Adjacent sequences:  A225003 A225004 A225005 * A225007 A225008 A225009 KEYWORD nonn AUTHOR R. H. Hardin, Apr 23 2013 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Feb 04 2017 STATUS approved

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Last modified October 14 12:02 EDT 2019. Contains 328004 sequences. (Running on oeis4.)