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A226012 Number of unimodal functions f:[n]->[2n]. 2
1, 2, 16, 161, 1716, 18832, 210574, 2385644, 27290916, 314537894, 3646709616, 42483615330, 496908084660, 5831654186256, 68636514069496, 809835178438996, 9575879777488676, 113445872396014898, 1346272950075766624, 16000494256911975827, 190424554847852203816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

a(n) ~ 5^(5*n-1/2) / (9*2^(8*n-5/2)*sqrt(Pi*n)). - Vaclav Kotesovec, Jul 16 2014

EXAMPLE

a(2) = 16: [1,1], [1,2], [1,3], [1,4], [2,1], [2,2], [2,3], [2,4], [3,1], [3,2], [3,3], [3,4], [4,1], [4,2], [4,3], [4,4].

MAPLE

a:= proc(n) option remember; `if`(n<3, 2^(n^2),

      ((2166498*n^7 -16827434*n^6 +54145990*n^5 -93141070*n^4

       +92008232*n^3 -51863736*n^2 +15330240*n -1814400) *a(n-1)

      -5*(5*n-9)*(5*n-8)*(5*n-7)*(5*n-6)

        *(333*n^3-595*n^2+338*n-60) *a(n-2)) / (16*(4*n-3)*

         (2*n-1)*(4*n-5)*(333*n^3-1594*n^2+2527*n-1326)*n))

    end:

seq(a(n), n=0..30);

CROSSREFS

Column k=2 of A226031.

Sequence in context: A009518 A052674 A259706 * A011552 A287222 A216598

Adjacent sequences:  A226009 A226010 A226011 * A226013 A226014 A226015

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 22 2013

STATUS

approved

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Last modified June 25 05:41 EDT 2019. Contains 324346 sequences. (Running on oeis4.)