

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
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OFFSET

0,2


COMMENTS

Kekule numbers for certain benzenoids.
a(n4), n>=4, is the number of ways to have n identical objects in m=4 of altogether n distinguishable boxes (n4 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)/(1x)^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



