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A107968
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a(n) = (n+1)*(n+2)^3*(n+3)^2*(n+4)*(3n+5)/1440.
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1
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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
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OFFSET
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0,2
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COMMENTS
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Kekulé numbers for certain benzenoids.
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LINKS
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FORMULA
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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)
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)
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MAPLE
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a:=n->(1/1440)*(n+1)*(n+2)^3*(n+3)^2*(n+4)*(3*n+5): seq(a(n), n=0..30);
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MATHEMATICA
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Table[(n + 1)*(n + 2)^3*(n + 3)^2*(n + 4)*(3 n + 5)/1440, {n, 0, 25}] (* Amiram Eldar, May 31 2022 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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