A226012 Number of unimodal functions f:[n]->[2n].

1, 2, 16, 161, 1716, 18832, 210574, 2385644, 27290916, 314537894, 3646709616, 42483615330, 496908084660, 5831654186256, 68636514069496, 809835178438996, 9575879777488676, 113445872396014898, 1346272950075766624, 16000494256911975827, 190424554847852203816

Offset: 0

Author

Alois P. Heinz, May 22 2013

Keywords

• nonn

Examples

			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].
		

Links

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

Crossrefs

Column k=2 of A226031.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, 2^(n^2),
      ((2166498*n^7 -16827434*n^6 [phone]*n^5 -93141070*n^4
       [phone]*n^3 -51863736*n^2 [phone]*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);

Mathematica

A[n_, k_] := If[n==0, 1, Sum[Binomial[n + 2j - 1, 2j], {j, 0, k n - 1}]];
a[n_] := A[n, 2];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz in A226031 *)

Formula

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