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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
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. 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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved