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Search: id:A006149
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| A006149 |
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Number of Dyck paths.
(Formerly M3634)
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+0
3
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| 1, 1, 4, 30, 330, 4719, 81796, 1643356, 37119160, 922268360, 24801924512, 713055329720, 21706243125300, 694280570551875, 23188541161342500, 804601696647424500, 28880966163870711000, 1068595748063216307000
(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 3X3 Hankel matrix [a_0, a_1, a_2 ; a_1, a_2, a_3 ; a_2, a_3, a_4] 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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G.f.: 4_F_3 ( [ 1, 1/2, 5/2, 3/2 ]; [ 4, 5, 6 ]; 64 x ).
a(n)=Det[Table[binomial[i+2, j-i+3], {i, 1, n}, {j, 1, n}]] - David Callan (callan(AT)stat.wisc.edu), Jul 20 2005
a(n) = 720 (2*n)! (2*n+2)! (2*n+4)! / (n! (n+1)! (n+2)! (n+3)! (n+4)! (n+5)!) - S. R. Finch (Steven.Finch(AT)inria.fr), Mar 30 2008
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CROSSREFS
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Sequence in context: A158834 A139086 A128329 this_sequence A121413 A001761 A099712
Adjacent sequences: A006146 A006147 A006148 this_sequence A006150 A006151 A006152
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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