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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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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)!) - Steven Finch (Steven.Finch(AT)inria.fr), Mar 30 2008
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CROSSREFS
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Adjacent sequences: A006146 A006147 A006148 this_sequence A006150 A006151 A006152
Sequence in context: A052574 A139086 A128329 this_sequence A121413 A001761 A099712
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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