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URL: https://oeis.org/A107959

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A107959
a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2 + 5*n + 5)/720.
1
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
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
LINKS
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229).
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 + 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
MAPLE
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);
MATHEMATICA
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 *)
PROG
(PARI) Vec((1 + 13*x + 28*x^2 + 13*x^3 + x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020
CROSSREFS
Sequence in context: A231749 A072040 A022682 * A200936 A110690 A020923
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved