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A006335
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4^n*(3*n)!/((n+1)!*(2*n+1)!).
(Formerly M2094)
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5
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1, 2, 16, 192, 2816, 46592, 835584, 15876096, 315031552, 6466437120, 136383037440, 2941129850880, 64614360416256, 1442028424527872, 32619677465182208, 746569714888605696, 17262927525017812992, 402801642250415636480, 9474719710174783733760, 224477974671833337692160
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of planar lattice walks of length 3n starting and ending at (0,0), remaining in the first quadrant and using only NE,W,S steps.
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REFERENCES
| G. Kreweras, Sur une classe de problemes de denombrement lies au treillis des partitions des entiers, Cahiers du Bureau Universitaire de Recherche Op\'{e}rationnelle, Institut de Statistique, Universit\'{e} de Paris, 6 (1965), circa p. 82.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| M. Bousquet-M\'elou, Walks in the quarter plane: Kreweras' algebraic model
M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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FORMULA
| G.f.: (1/(12*x)) * (hypergeom([ -2/3, -1/3],[1/2],27*x)-1) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 02 2009]
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MATHEMATICA
| aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, 3 n], {n, 0, 25}] - Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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PROG
| (PARI) a(n)=if(n<0, 0, 4^n*(3*n)!/(n+1)!/(2*n+1)!)
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CROSSREFS
| Equals 2^(n-1) * A000309(n-1) for n>1.
Cf. A098272. First row of array A098273.
Sequence in context: A123898 A118644 A183205 * A051711 A012683 A012677
Adjacent sequences: A006332 A006333 A006334 * A006336 A006337 A006338
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 20 2008 at the suggestion of R. J. Mathar
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