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A108647 (n+1)^2*(n+2)^2*(n+3)^2*(n+4)/144. 3
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Kekule numbers for certain benzenoids.

a(n-4), n>=4, is the number of ways to have n identical objects in m=4 of altogether n distinguishable boxes (n-4 boxes stay empty). - W. Lang, Nov 13 2007

REFERENCES

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).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(n)=C(n+4,4)*C(n+3,2)(n+1)/3; - Paul Barry, 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, May 09 2008

EXAMPLE

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

MAPLE

a:=(n+1)^2*(n+2)^2*(n+3)^2*(n+4)/144: seq(a(n), n=0..30);

PROG

(Mupad) 4*binomial(n, 4)^2/n $ n = 4..35; - Zerinvary Lajos, May 09 2008

(Haskell)

a108647 = flip a103371 3 . (+ 3)  -- Reinhard Zumkeller, Apr 04 2014

CROSSREFS

Fourth column of triangle A103371.

Sequence in context: A100190 A189494 A022680 * A164605 A000492 A015866

Adjacent sequences:  A108644 A108645 A108646 * A108648 A108649 A108650

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jun 13 2005

STATUS

approved

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Last modified July 24 21:14 EDT 2014. Contains 244897 sequences.