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A006150
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Number of Dyck paths.
(Formerly M4013)
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3
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1, 1, 5, 55, 1001, 26026, 884884, 37119160, 1844536720, 105408179176, 6774025632340, 481155055944150, 37259723952950625, 3111129272480118750, 277587585343361452500, 26268551497229678505000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the determinant of the 4X4 Hankel matrix [a_0, a_1, a_2, a_3 ; a_1, a_2, a_3, a_4 ; a_2, a_3, a_4, a_5 ; a_3, a_4, a_5, a_6] with a_j=A000108(n+j) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 12 2007
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REFERENCES
| S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 183).
M. de Sainte-Catherine, Couplages et Pfaffiens en Combinatoire. Physique et Informatique. Ph.D Dissertation, Universit\'{e} Bordeaux I, 1983.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(n)=Det[Table[binomial[i+3, j-i+4], {i, 1, n}, {j, 1, n}]] - David Callan (callan(AT)stat.wisc.edu), Jul 20 2005
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MAPLE
| with (linalg): ctln:= proc(n) option remember; binomial (2*n, n)/ (n+1) end: a:= n-> det (Matrix(4, (i, j)-> ctln (i+j-2+n))): seq (a(n), n=0..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 10 2008]
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CROSSREFS
| Sequence in context: A135861 A141361 A203013 * A140049 A130031 A119399
Adjacent sequences: A006147 A006148 A006149 * A006151 A006152 A006153
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 10 2008
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