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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 Table of n, a(n) for n=0..25. Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). 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 Adjacent sequences: A109120 A109121 A109122 * A109124 A109125 A109126 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.)