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A134288
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Binomial(n+7,7)*binomial(n+7,6)/(n+7).
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4
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1, 28, 336, 2520, 13860, 60984, 226512, 736164, 2147145, 5725720, 14158144, 32821152, 71954064, 150233760, 300467520, 578399976, 1075994073, 1941008916, 3405278800, 5824819000, 9735768900, 15931258200, 25565576400, 40293571500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Seventh column of Narayana triangle A001263.
In the Narayana triangle N(n,k)= A001263(n,k) the sequence of column nr. k>=1 (without leading zeros coincides with the sequence of the diagonal d=k-1>=0 (d=0 for the main diagonal N(n,n)).
Kekul\'e numbers K(O(1,6,n)) for certain benzenoids (see the Cyvin-Gutman reference, p. 105, eq. (i)).
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REFERENCES
| S. J. Cyvin and I. Gutman, Kekul\'e structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988.
S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; Prop. 8.4, case n=8. - N. J. A. Sloane, Aug 28 2010.
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FORMULA
| a(n)= A001263(n+7,7).
O.g.f.: (1+15*x+50*x^2+50*x^3+15*x^4+x^5)/(1-x)^13. Numerator polynomial is the sixth row polynomial of the Narayana triangle.
a(n)= binomial(n+6,6)^2 - binomial(n+6,5)*binomial(n+6,7). [From Gary Detlefs, Dec 05 2011]
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CROSSREFS
| Cf. A108679 (sixth column of Narayana triangle).
Cf. A134289 (eighth column of Narayana triangle).
Sequence in context: A159520 A027820 A092713 * A200968 A010833 A022720
Adjacent sequences: A134285 A134286 A134287 * A134289 A134290 A134291
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 13 2007
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EXTENSIONS
| Edited by N. J. A. Sloane, Aug 28 2010
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