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A109123 a(n) = 4*(n+1)^2*(n+3)^2*(5*n^2 + 20*n + 12). 0
432, 9472, 64800, 269568, 842800, 2184192, 4953312, 10163200, 19288368, 34387200, 58238752, 94493952, 147841200, 224186368, 330847200, 476762112, 672713392, 931564800, 1268513568, 1701356800, 2250772272, 2940613632, 3798220000, 4854739968, 6145470000, 7710207232 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Kekulé numbers for certain benzenoids.
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 311).
LINKS
FORMULA
G.f.: 16*(27 + 403*x + 473*x^2 - 15*x^3 + 14*x^4 - 2*x^5)/(1-x)^7.
From Amiram Eldar, Jun 02 2022: (Start)
Sum_{n>=0} 1/a(n) = 197/864 - Pi^2/144 - (5/144)*sqrt(5/2)*Pi*cot(2*sqrt(2/5)*Pi).
Sum_{n>=0} (-1)^n/a(n) = -85/432 - Pi^2/288 - (5/144)*sqrt(5/2)*Pi*cosec(2*sqrt(2/5)*Pi). (End)
MAPLE
a:=n->4*(n+1)^2*(n+3)^2*(5*n^2+20*n+12): seq(a(n), n=0..28);
MATHEMATICA
Table[4*(n + 1)^2*(n + 3)^2*(5*n^2 + 20*n + 12), {n, 0, 30}] (* Amiram Eldar, Jun 02 2022 *)
CROSSREFS
Sequence in context: A223595 A223436 A230922 * A223688 A269183 A228105
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved

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Last modified April 19 15:03 EDT 2024. Contains 371794 sequences. (Running on oeis4.)