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A006151
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Number of Dyck paths.
(Formerly M4288)
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3
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1, 1, 6, 91, 2548, 111384, 6852768, 553361016, 55804330152, 6774025632340, 962310111888300, 156490840602392625, 28622389306817092500, 5804104057179375825000, 1289547073500366035700000
(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 5X5 Hankel matrix [a_0, a_1, a_2, a_3, a_4 ; a_1, a_2, a_3, a_4, a_5 ; a_2, a_3, a_4, a_5, a_6 ; a_3, a_4, a_5, a_6, a_7 ; a_4, a_5, a_6, a_7, a_8] 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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MAPLE
| with (linalg): ctln:= proc(n) option remember; binomial (2*n, n)/ (n+1) end: a:= n-> det (Matrix(5, (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: A013297 A077370 A095864 * A005327 A171910 A113266
Adjacent sequences: A006148 A006149 A006150 * A006152 A006153 A006154
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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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