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 A107968 a(n) = (n+1)*(n+2)^3*(n+3)^2*(n+4)*(3n+5)/1440. 1
 1, 24, 220, 1225, 4998, 16464, 46368, 115830, 263175, 553696, 1093092, 2045407, 3656380, 6283200, 10431744, 16802460, 26346141, 40330920, 60421900, 88774917, 128146018, 182018320, 254748000, 351731250, 479594115, 646407216, 861927444 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Kekulé numbers for certain benzenoids. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230). Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA From Colin Barker, Apr 22 2020: (Start) G.f.: (1 + 15*x + 40*x^2 + 25*x^3 + 3*x^4) / (1 - x)^9. a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8. (End) From Amiram Eldar, May 31 2022: (Start) Sum_{n>=0} 1/a(n) = 7895/7 + 10935*sqrt(3)*Pi/14 + 150*Pi^2 - 98415*log(3)/14 + 720*zeta(3). Sum_{n>=0} (-1)^n/a(n) = 2875/7 + 10935*sqrt(3)*Pi/7 - 105*Pi^2 - 72960*log(2)/7 - 540*zeta(3). (End) MAPLE a:=n->(1/1440)*(n+1)*(n+2)^3*(n+3)^2*(n+4)*(3*n+5): seq(a(n), n=0..30); MATHEMATICA Table[(n + 1)*(n + 2)^3*(n + 3)^2*(n + 4)*(3 n + 5)/1440, {n, 0, 25}] (* Amiram Eldar, May 31 2022 *) PROG (PARI) Vec((1 + 15*x + 40*x^2 + 25*x^3 + 3*x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020 CROSSREFS Sequence in context: A042112 A297679 A202073 * A269777 A024302 A181710 Adjacent sequences: A107965 A107966 A107967 * A107969 A107970 A107971 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified November 30 12:40 EST 2022. Contains 358441 sequences. (Running on oeis4.)