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Search: id:A108679
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| A108679 |
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(n+1)(n+2)^2*(n+3)^2*(n+4)^2*(n+5)^2*(n+6)/86400. |
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+0
3
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| 1, 21, 196, 1176, 5292, 19404, 60984, 169884, 429429, 1002001, 2186184, 4504864, 8836464, 16604784, 30046752, 52581816, 89311761, 147685461, 238369516, 376372920, 582481900, 885069900, 1322357400, 1945206900, 2820550005
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Kekule numbers for certain benzenoids.
6th column of the table of Narayana numbers A001263 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 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 (p.232, # 1).
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FORMULA
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a(n)= A001263(n+6,6) = binomial(n+5, 5)*binomial(n+6, 5)/6 = binomial(n+6,6)*binomial(n+6,5)/(n+6).
G.f.=(1+10z+20z^2+10z^3+z^4)/(1-z)^11. Numerator polynomial is the fifth row polynomial of the Narayana triangle.
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MAPLE
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a:=n->(n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)^2*(n+6)/86400: seq(a(n), n=0..30);
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CROSSREFS
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Sequence in context: A163718 A164606 A027780 this_sequence A058086 A159857 A125384
Adjacent sequences: A108676 A108677 A108678 this_sequence A108680 A108681 A108682
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 17 2005
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