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Search: id:A006150
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| A006150 |
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Number of Dyck paths.
(Formerly M4013)
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+0
3
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| 1, 1, 5, 55, 1001, 26026, 884884, 37119160, 1844536720, 105408179176, 6774025632340, 481155055944150, 37259723952950625, 3111129272480118750, 277587585343361452500, 26268551497229678505000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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. Phys-ique et Informatique. Ph.D Dissertation, Universit\'{e} Bordeaux I, 1983.
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FORMULA
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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
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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
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Sequence in context: A155807 A135861 A141361 this_sequence A140049 A130031 A119399
Adjacent sequences: A006147 A006148 A006149 this_sequence A006151 A006152 A006153
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 10 2008
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