|
%I #19 Mar 26 2014 16:39:21
%S 5,16,68,392,2905,25508,251188,2703440,31462590,393962080,5289624824,
%T 75921813328,1161309733909,18873565250876,324948587103540,
%U 5910550393881120,113284096799562930,2282403914428653360,48231478277117432040,1066811449438992210000
%N Number of permutations of n letters in the class Av_n(213;2).
%H Vaclav Kotesovec, <a href="/A220903/b220903.txt">Table of n, a(n) for n = 3..400</a>
%H Filippo Disanto and Thomas Wiehe, <a href="http://arxiv.org/abs/1210.6908">Some instances of a sub-permutation problem on pattern avoiding permutations</a>, arXiv preprint arXiv:1210.6908, 2012 (see Prop. 8).
%F Recurrence (for n>=6): (n-3)*(n+1)*(n^2 - 8*n + 10)*a(n) = (2*n^5 - 19*n^4 + 38*n^3 + 45*n^2 - 174*n + 120)*a(n-1) - (n-1)*(n^5 - 5*n^4 - 35*n^3 + 249*n^2 - 462*n + 240)*a(n-2) + 2*(n-4)*(n-2)*(n-1)*(2*n - 5)*(n^2 - 6*n + 3)*a(n-3). - _Vaclav Kotesovec_, Mar 20 2014
%F a(n) ~ n! * (1 - 2*exp(2)*BesselI(1,2)/n^2). - _Vaclav Kotesovec_, Mar 26 2014
%t RecurrenceTable[{2 (-4+n) (-2+n) (-1+n) (-5+2 n) (3-6 n+n^2) a[-3+n]-(-1+n) (240-462 n+249 n^2-35 n^3-5 n^4+n^5) a[-2+n]+(120-174 n+45 n^2+38 n^3-19 n^4+2 n^5) a[-1+n]-(-3+n) (1+n) (10-8 n+n^2) a[n]==0,a[3]==5,a[4]==16,a[5]==68},a,{n,3,20}] (* _Vaclav Kotesovec_, Mar 26 2014 *)
%o (PARI)
%o catalan(n) = {binomial(2*n, n)/(n+1);}
%o a(n) = { n! - (2*(n-2)!*sum(i=1, n-4, catalan(i)/(i-1)!)+ 2*(n-2)*(n-3)*catalan(n-3)+ 2*(n-2)*catalan(n-2)-catalan(n)+2*catalan(n-1));}
%o \\ _Michel Marcus_, Feb 07 2013
%K nonn
%O 3,1
%A _N. J. A. Sloane_, Jan 01 2013
%E More terms from _Michel Marcus_, Feb 07 2013
|
