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%I
%S 1,1,2,6,23,102,495,2549,13682,75714,428882,2474573,14492346,85926361,
%T 514763279,3111119358,18946375767,116147683902,716179441293,
%U 4438862153246,27638747494178,172805469880497,1084462349973559,6828717036765622,43132158190994223,273204023401012901
%N Number of permutations of [1..n] which avoid 4231 and 42513.
%C (a(n))_{n>=1} is the INVERT transform of (u(n))_{n>=1}:=(1,1,3,12,55,273,...), the ternary numbers A001764. - David Callan Nov 21 2011
%C a(n) = number of Dyck paths of semilength 2n for which all descents are of even length (counted by A001764) with no valley vertices at height 1. For example, a(2)=2 counts UUUUDDDD, UUDDUUDD. - David Callan, Nov 21 2011
%D M. H. Albert et al., Restricted permutations and queue jumping, Discrete Math., 287 (2004), 129-133.
%F G.f.: 1+Sum( t^n * Sum( (n-l)*binomial(2*l+n, l)/(2*l+n), l=0..n ), n=1..oo).
%F G.f.: sqrt(3)/(sqrt(3)-2*sqrt(x)*sin(asin(3*sqrt(3x)/2)/3)); - _Paul Barry_, Dec 15 2006
%F Let M = the production matrix:
%F 1, 1
%F 1, 2, 1
%F 1, 3, 2, 1
%F 1, 4, 3, 2, 1
%F 1, 5, 4, 3, 2, 1
%F ...
%F a(n) = upper left term in M^n, with sum of top row terms = a(n+1). Example: top row of M^3 = (6, 11, 5, 1), where a(3) = 6 and a(4) = 23 = (6 + 11 + 5 + 1). - Gary W. Adamson, Jul 07 2011
%p 1+add( t^n * add( (n-l)*binomial(2*l+n,l)/(2*l+n), l=0..n ), n=1..30);
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Oct 30 2004
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