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A037952
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C(n, [(n-1)/2]).
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16
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0, 1, 1, 3, 4, 10, 15, 35, 56, 126, 210, 462, 792, 1716, 3003, 6435, 11440, 24310, 43758, 92378, 167960, 352716, 646646, 1352078, 2496144, 5200300, 9657700, 20058300, 37442160, 77558760, 145422675, 300540195, 565722720, 1166803110, 2203961430
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| First differences of central binomial coefficients: a(n)=A001405(n+1)-A001405(n).
The maximum size of an intersecting (or proper) antichain on an n-set - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
Number of ordered trees with n+1 edges, having root of degree at least 2 and nonroot nodes of outdegree 0 or 2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 02 2002
a(n)=number of Dyck (n+1)-paths that are symmetric but not prime. A prime Dyck path is one that returns to the x-axis only at its terminal point. For example a(3)=3 counts UDUUDDUD, UUDDUUDD, UDUDUDUD. - David Callan (callan(AT)stat.wisc.edu), Dec 09 2004
Number of involutions of [n+2] containing the pattern 132 exactly once. For example, a(3)=3 because we have 1'3'2'45, 42'5'13' and 52'4'3'1 (the entries corresponding to the pattern 132 are "primed"). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 17 2005
Also number of ways to put n eggs in floor(n/2) baskets where order of the baskets matters and all baskets have at least 1 egg. - Ben Thurston (benthurston27(AT)yahoo.com), Sep 30 2006
[1,1,3,4,10,15,35,56,...] is the convolution of A001405 with A126120 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 17 2007
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REFERENCES
| J.-L. Baril, Classical sequences revisited with permutations avoiding dotted pattern, Electronic Journal of Combinatorics, 18 (2011), #P178; http://www.combinatorics.org/Volume_18/PDF/v18i1p178.pdf.
E. Deutsch, Ordered trees with prescribed root degrees, node degrees and branch lengths, Discrete Math., 282, 2004, 89-94.
O. Guibert and T. Mansour, Restricted 132-involutions, Sem. Lotharingien de Combinatoire, 48, 2002, Article B48a (Corollary 4.2).
M. van der Vel, Determination of msd(L^n), J. Algebraic Combin., 9 (1999), 161-171.
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LINKS
| M. Miyakawa, A. Nozaki, G. Pogosyan, I. G. Rosenberg, A map from the lower-half of the n-Cube onto the (n-1)-Cube which preserves intersecting antichains, Discr. Appl. Math. 92 (2-3) (1999) 223-228.
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FORMULA
| E.g.f.: BesselI(1, 2*x)+BesselI(2, 2*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2003
O.g.f.: [1-sqrt(1-4x^2)]/[x-2x^2+x*sqrt(1-4x^2)].
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CROSSREFS
| Cf. A032263, A051303-A051307, A001405.
Cf. A047171, A036256, A051920.
Sequence in context: A054184 A188022 A007007 * A093512 A081160 A051437
Adjacent sequences: A037949 A037950 A037951 * A037953 A037954 A037955
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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