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

%I A226012 #14 Dec 20 2020 08:06:26
%S A226012 1,2,16,161,1716,18832,210574,2385644,27290916,314537894,3646709616,
%T A226012 42483615330,496908084660,5831654186256,68636514069496,
%U A226012 809835178438996,9575879777488676,113445872396014898,1346272950075766624,16000494256911975827,190424554847852203816
%N A226012 Number of unimodal functions f:[n]->[2n].
%H A226012 Alois P. Heinz, <a href="/A226012/b226012.txt">Table of n, a(n) for n = 0..500</a>
%F A226012 a(n) ~ 5^(5*n-1/2) / (9*2^(8*n-5/2)*sqrt(Pi*n)). - _Vaclav Kotesovec_, Jul 16 2014
%e A226012 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].
%p A226012 a:= proc(n) option remember; `if`(n<3, 2^(n^2),
%p A226012       ((2166498*n^7 -16827434*n^6 +54145990*n^5 -93141070*n^4
%p A226012        +92008232*n^3 -51863736*n^2 +15330240*n -1814400) *a(n-1)
%p A226012       -5*(5*n-9)*(5*n-8)*(5*n-7)*(5*n-6)
%p A226012         *(333*n^3-595*n^2+338*n-60) *a(n-2)) / (16*(4*n-3)*
%p A226012          (2*n-1)*(4*n-5)*(333*n^3-1594*n^2+2527*n-1326)*n))
%p A226012     end:
%p A226012 seq(a(n), n=0..30);
%t A226012 A[n_, k_] := If[n==0, 1, Sum[Binomial[n + 2j - 1, 2j], {j, 0, k n - 1}]];
%t A226012 a[n_] := A[n, 2];
%t A226012 a /@ Range[0, 30] (* _Jean-François Alcover_, Dec 20 2020, after _Alois P. Heinz_ in A226031 *)
%Y A226012 Column k=2 of A226031.
%K A226012 nonn
%O A226012 0,2
%A A226012 _Alois P. Heinz_, May 22 2013