0,2

Kekul\'e numbers for certain benzenoids.

a(n)=K(L(n))*K(O(2,4,n)) with the Cyvin and Gutman Kekul\'e number notation. See p. 62 for the L(n) structure with K(L(n))=n+1 and p. 105 (i) for the O(k,m,n) structure and its Kekul/'e number. This corresponds to an essentially disconnected 7-tier benzenoid structure similar to the 6-tier structure shown on p. 230, nr.23 (see A108647).

a(n-5), n>=5, is the number of ways to put n identical objects into m=5 of alltogether n distinguishable boxes (n-5 boxes stay empty).

S. J. Cyvin and I. Gutman, Kekul\'e structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988.

a(n)=A103371(n+4,4),n>=0.

a(n)=((n+1)*(n+2)*(n+3)*(n+4))^2*(n+5)/2880, n>=0. 2880=4!*5!=A010790(4).

G.f.: (1+20*x+60*x^2+40*x^3+5*x^4)/(1-x)^10. Numerator polynomial from fifth row of triangle A132813.

a(n)= 5*C(n,5)^2/n, n>= 5. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008

a(2)=315 because n=7 identical balls can be put into m=5 of n=7 distinguishable boxes in

binomial(7,5)*(5!/(4!*1!)+ 5!/(3!*2!)) = 21*(5+10) = 315 ways. The m=5 part partitions of 7, namely (1^4,3) and (1^3,2^2) specify the filling of each of the 21 possible five box choices. W. Lang, Nov 13 2007.

(Mupad) 5*binomial(n, 5)^2/n $ n = 5..35; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008

Cf. A108647 (fourth column of triangle A103371).

Adjacent sequences: A134284 A134285 A134286 this_sequence A134288 A134289 A134290

Sequence in context: A126551 A042750 A074994 this_sequence A141216 A006859 A107967

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 13 2007