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Search: id:A108647
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| A108647 |
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(n+1)^2*(n+2)^2*(n+3)^2*(n+4)/144. |
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+0
3
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| 1, 20, 150, 700, 2450, 7056, 17640, 39600, 81675, 157300, 286286, 496860, 828100, 1332800, 2080800, 3162816, 4694805, 6822900, 9728950, 13636700, 18818646, 25603600, 34385000, 45630000, 59889375, 77808276, 100137870, 127747900
(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.
a(n-4), n>=4, is the number of ways to have n identical objects in m=4 of alltogether n distinguishable boxes (n-4 boxes stay empty). W. Lang, Nov 13 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.230, no. 23).
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FORMULA
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a(n)=C(n+4,4)*C(n+3,2)(n+1)/3; - Paul Barry (pbarry(AT)wit.ie), May 13 2006
G.f.: (1+12*x+18*x^2+4*x^3)/(1-x)^8.
a(n)= 4*C(n,4)^2/n, n >= 4. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008
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EXAMPLE
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a(2)=150 because n=6 identical balls can be put into m=4 of n=6 distinguishable boxes in binomial(6,4)*(4!/(3!*1!)+ 4!/(2!*2!)) = 15*(4 + 6) =150 ways. The m=4 part partitions of 6, namely (1^3,3) and (1^2,2^2) specify the filling of each of the 15 possible four box choices. W. Lang, Nov 13 2007.
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MAPLE
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a:=(n+1)^2*(n+2)^2*(n+3)^2*(n+4)/144: seq(a(n), n=0..30);
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PROGRAM
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(Mupad) 4*binomial(n, 4)^2/n $ n = 4..35; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008
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CROSSREFS
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Fourth column of triangle A103371.
Sequence in context: A094171 A100190 A022680 this_sequence A164605 A000492 A015866
Adjacent sequences: A108644 A108645 A108646 this_sequence A108648 A108649 A108650
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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 13 2005
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