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 A107970 a(n) = (n+1)*(n+2)^3*(n+3)*(2n+3)*(2n+5)/360. 0
 1, 21, 168, 825, 3003, 8918, 22848, 52326, 109725, 214291, 394680, 692055, 1163799, 1887900, 2968064, 4539612, 6776217, 9897537, 14177800, 19955397, 27643539, 37742034, 50850240, 67681250, 89077365, 116026911, 149682456, 191380483 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS KekulĂ© numbers for certain benzenoids. REFERENCES S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230). LINKS Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1). FORMULA G.f.: (x^4+13*x^3+28*x^2+13*x+1)/(x-1)^8. - Colin Barker, Sep 21 2012 From Amiram Eldar, May 31 2022: (Start) Sum_{n>=0} 1/a(n) = 360*zeta(3) - 3840*log(2) + 2230. Sum_{n>=0} (-1)^n/a(n) = 1490 - 1680*log(2) - 270*zeta(3). (End) MAPLE a:=n->(1/360)*(n+1)*(n+2)^3*(n+3)*(2*n+3)*(2*n+5): seq(a(n), n=0..32); MATHEMATICA Table[(n + 1)*(n + 2)^3*(n + 3)*(2 n + 3)*(2 n + 5)/360, {n, 0, 25}] (* Amiram Eldar, May 31 2022 *) CROSSREFS Sequence in context: A332944 A022681 A266733 * A105249 A278992 A041848 Adjacent sequences:  A107967 A107968 A107969 * A107971 A107972 A107973 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified July 5 23:40 EDT 2022. Contains 355108 sequences. (Running on oeis4.)