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A226013 Number of unimodal functions f:[n]->[2n] with f(1)<>1 and f(i)<>f(i+1).

%I A226013 #17 Jul 16 2014 10:19:47
%S A226013 1,1,9,70,581,4956,43065,379093,3369301,30168268,271716644,2459014504,
%T A226013 22342432139,203682343840,1862165051700,17066961406095,
%U A226013 156758478514005,1442549386731900,13297258924349292,122757267172891048,1134800963513922996,10503230892143398192
%N A226013 Number of unimodal functions f:[n]->[2n] with f(1)<>1 and f(i)<>f(i+1).
%H A226013 Alois P. Heinz, <a href="/A226013/b226013.txt">Table of n, a(n) for n = 0..500</a>
%F A226013 a(n) ~ 2^(8*n-3/2) / (7*sqrt(Pi*n)*3^(3*n-3/2)). - _Vaclav Kotesovec_, Jul 16 2014
%F A226013 Recurrence (of order 2): 6*n*(3*n - 4)*(3*n - 2)*(77*n^2 - 244*n + 191)*a(n) = (37345*n^5 - 212742*n^4 + 463115*n^3 - 476646*n^2 + 228792*n - 40320)*a(n-1) + 8*(2*n - 3)*(4*n - 7)*(4*n - 5)*(77*n^2 - 90*n + 24)*a(n-2). - _Vaclav Kotesovec_, Jul 16 2014
%e A226013 a(0) = 1: [].
%e A226013 a(1) = 1: [2].
%e A226013 a(2) = 9: [2,1], [2,3], [2,4], [3,1], [3,2], [3,4], [4,1], [4,2], [4,3].
%e A226013 a(3) = 70: [2,3,1], [2,3,2], [2,3,4], ..., [6,5,2], [6,5,3], [6,5,4].
%e A226013 a(4) = 581: [2,3,2,1], [2,3,4,1], [2,3,4,2], ..., [8,7,6,3], [8,7,6,4], [8,7,6,5].
%p A226013 a:= proc(n) option remember; `if`(n<3, (2*n-1)^2,
%p A226013      ((49421666742*n^4 -205832874348*n^3 +295740702162*n^2
%p A226013        -167673767628*n +29628103680) *a(n-1)
%p A226013       +(27981954763*n^4 -127816385262*n^3 +231525900473*n^2
%p A226013        -221063690262*n +102518080560) *a(n-2)
%p A226013       +29529976*(2*n-5)*(4*n-9)*(n-3)*(4*n-11) *a(n-3))
%p A226013       / (288*n*(2131486*n-3539195)*(3*n-4)*(3*n-2)))
%p A226013     end:
%p A226013 seq(a(n), n=0..30);
%Y A226013 Cf. A014301 (functions f:[n]->[n] with f(1)<>1 and f(i)<>f(i+1)).
%K A226013 nonn
%O A226013 0,3
%A A226013 _Alois P. Heinz_, May 22 2013