OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = (1/17280)(n+1)(n+2)^3*(n+3)^3*(n+4)^2*(n+5).
G.f.: -(2*x^5+28*x^4+85*x^3+75*x^2+19*x+1)/(x-1)^11. - Colin Barker, Sep 20 2012
From Amiram Eldar, May 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 1400*Pi^2 + 2880*zeta(3) - 51835/3.
Sum_{n>=0} (-1)^n/a(n) = 20*Pi^2 + 28160*log(2) + 4320*zeta(3) - 74725/3. (End)
MAPLE
a:=n->(1/12)*binomial(n+3, 2)*binomial(n+4, 3)*binomial(n+5, 5): seq(a(n), n=0..30);
MATHEMATICA
a[n_] := Binomial[n + 3, 2] * Binomial[n + 4, 3] * Binomial[n + 5, 5]/12; Array[a, 25, 0] (* Amiram Eldar, May 29 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved