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A110127
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Number of EE's crossing the line y=x (i.e. two consecutive E steps from the line y=x+1 to the line y=x-1) in all Delannoy paths of length n (a Delannoy path of length n is a path from (0,0) to (n,n), consisting of steps E=(1,0), N=(0,1) and D=(1,1)).
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3
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0, 0, 1, 10, 75, 508, 3277, 20566, 126871, 773688, 4679769, 28136546, 168395235, 1004239156, 5971820709, 35429993390, 209800355631, 1240361694064, 7323260678065, 43187703202234, 254439363998587, 1497730375793004
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n)=sum(k*A110121(n,k),k=0..floor(n/2)).
{A110127}[n+2] = conv({0, {A002002})[n] [From Tilman Neumann (Tilman.Neumann(AT)web.de), Feb 05 2009]
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REFERENCES
| R. A. Sulanke, Objects counted by the central Delannoy numbers, J. of Integer Sequences, 6, 2003, Article 03.1.5.
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FORMULA
| G.f.=z^2*R^2/(1-6z+z^2), where R=1+zR+zR^2=[1-z-sqrt(1-6z+z^2)]/(2z) is the g.f. of the large Schroeder numbers (A006318).
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EXAMPLE
| a(2)=1 because, among the 13 (=A001850(2)) Delannoy paths of length 2, only NEEN has an EE crossing the line y=x.
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MAPLE
| R:=(1-z-sqrt(1-6*z+z^2))/2/z: G:=z^2*R^2/(1-6*z+z^2): Gser:=series(G, z=0, 27): 0, seq(coeff(Gser, z^n), n=1..24);
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CROSSREFS
| Cf. A001850, A110121.
Sequence in context: A053464 A111998 A026935 * A081017 A025015 A049392
Adjacent sequences: A110124 A110125 A110126 * A110128 A110129 A110130
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 13 2005
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