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A006149
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Number of Dyck paths.
(Formerly M3634)
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
Third subdiagonal in A123352, equivalent to the 6th subdiagonal in A185249, its "aerated" version with additional subdiagonals entirely filled with zeros. - R. J. Mathar, Feb 18 2011
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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
| 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
| Sequence in context: A139086 A180623 A128329 * A121413 A001761 A099712
Adjacent sequences: A006146 A006147 A006148 * A006150 A006151 A006152
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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