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A134290
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Ninth column (and diagonal) of Narayana triangle A001263.
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7
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1, 45, 825, 9075, 70785, 429429, 2147145, 9202050, 34763300, 118195220, 367479684, 1057896060, 2848181700, 7229999700, 17420856420, 40067969766, 88385227425, 187746398125, 385374185625, 766691800875, 1482270815025, 2791289197125, 5130235085625, 9219552907500
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OFFSET
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0,2
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COMMENTS
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See a comment under A134288 on the coincidence of column and diagonal sequences.
Kekul\'e numbers K(O(1,8,n)) for certain benzenoids (see the Cyvin-Gutman reference, p. 105, eq. (i)).
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekul\'e structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n)= A001263(n+9,9) = binomial(n+9,9)*binomial(n+9,8)/(n+9).
O.g.f.: P(8,x)/(1-x)^17 with the numerator polynomial P(8,x)=sum(A001263(8,k)*x^(k-1),k=1..8), the eighth row polynomial of the Narayana triangle. P(8,x)=1+28*x+196*x^2+490*x^3+490*x^4+196*x^5+28*x^6+x^7.
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CROSSREFS
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Cf. A134289 (eighth column of Narayana triangle).
Cf. A134291 (tenth column of Narayana triangle).
Sequence in context: A105251 A099632 A024379 * A078761 A034967 A199352
Adjacent sequences: A134287 A134288 A134289 * A134291 A134292 A134293
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang Nov 13 2007
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STATUS
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approved
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