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A107959
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a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2 + 5*n + 5)/720.
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1
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1, 22, 190, 1015, 4018, 12936, 35784, 88110, 197835, 412126, 806806, 1498861, 2662660, 4550560, 7518624, 12058236, 18834453, 28731990, 42909790, 62865187, 90508726, 128250760, 179101000, 246782250, 335859615, 451886526, 601568982
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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 + 13*x + 28*x^2 + 13*x^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) = 120*Pi^2 - 144*sqrt(5)*Pi*tan(sqrt(5)*Pi/2) - 790. - Amiram Eldar, May 31 2022
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MAPLE
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a:=n->(1/720)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2+5*n+5): seq(a(n), n=0..30);
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MATHEMATICA
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Table[(n+1)(n+2)^2(n+3)^2(n+4)(n^2+5n+5)/720, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 22, 190, 1015, 4018, 12936, 35784, 88110, 197835}, 30] (* Harvey P. Dale, Sep 27 2020 *)
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PROG
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(PARI) Vec((1 + 13*x + 28*x^2 + 13*x^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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