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A098746
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Number of permutations of [1..n] which avoid 4231 and 42513.
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4
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1, 1, 2, 6, 23, 102, 495, 2549, 13682, 75714, 428882, 2474573, 14492346, 85926361, 514763279, 3111119358, 18946375767, 116147683902, 716179441293, 4438862153246, 27638747494178, 172805469880497, 1084462349973559, 6828717036765622, 43132158190994223, 273204023401012901
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OFFSET
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0,3
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COMMENTS
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(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
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
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REFERENCES
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M. H. Albert et al., Restricted permutations and queue jumping, Discrete Math., 287 (2004), 129-133.
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LINKS
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Table of n, a(n) for n=0..25.
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FORMULA
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G.f.: 1+Sum( t^n * Sum( (n-l)*binomial(2*l+n, l)/(2*l+n), l=0..n ), n=1..oo).
G.f.: sqrt(3)/(sqrt(3)-2*sqrt(x)*sin(asin(3*sqrt(3x)/2)/3)); - Paul Barry, Dec 15 2006
Let M = the production matrix:
1, 1
1, 2, 1
1, 3, 2, 1
1, 4, 3, 2, 1
1, 5, 4, 3, 2, 1
...
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
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MAPLE
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1+add( t^n * add( (n-l)*binomial(2*l+n, l)/(2*l+n), l=0..n ), n=1..30);
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CROSSREFS
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Sequence in context: A218225 A120346 A050389 * A088929 A174193 A022558
Adjacent sequences: A098743 A098744 A098745 * A098747 A098748 A098749
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Oct 30 2004
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STATUS
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approved
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