login
A109116
a(n) = (n+1)^3*(n+2)^2*(n+5).
1
20, 432, 3024, 12800, 40500, 105840, 241472, 497664, 947700, 1694000, 2874960, 4672512, 7320404, 11113200, 16416000, 23674880, 33428052, 46317744, 63102800, 84672000, 112058100, 146452592, 189221184, 241920000, 306312500, 384387120
OFFSET
0,1
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. 310).
FORMULA
G.f.: 4(5 + 73x + 105x^2 + x^3 - 4x^4)/(1-x)^7.
From Amiram Eldar, May 31 2022: (Start)
Sum_{n>=0} 1/a(n) = 8473/6912 - 43*Pi^2/288 + zeta(3)/4.
Sum_{n>=0} (-1)^n/a(n) = 16*log(2)/9 + 3*zeta(3)/16 - 11*Pi^2/576 - 8441/6912. (End)
MAPLE
a:=n->(n+1)^3*(n+2)^2*(n+5): seq(a(n), n=0..30);
MATHEMATICA
Table[(n+1)^3 (n+2)^2 (n+5), {n, 0, 30}] (* Harvey P. Dale, Sep 24 2011 *)
PROG
(Magma) [(n+1)^3*(n+2)^2*(n+5): n in [0..30]]; // Vincenzo Librandi, Sep 25 2011
CROSSREFS
Sequence in context: A215290 A130832 A180810 * A190922 A136257 A320765
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved