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A107970
a(n) = (n+1)*(n+2)^3*(n+3)*(2n+3)*(2n+5)/360.
0
1, 21, 168, 825, 3003, 8918, 22848, 52326, 109725, 214291, 394680, 692055, 1163799, 1887900, 2968064, 4539612, 6776217, 9897537, 14177800, 19955397, 27643539, 37742034, 50850240, 67681250, 89077365, 116026911, 149682456, 191380483
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. 230).
FORMULA
G.f.: (x^4+13*x^3+28*x^2+13*x+1)/(x-1)^8. - Colin Barker, Sep 21 2012
From Amiram Eldar, May 31 2022: (Start)
Sum_{n>=0} 1/a(n) = 360*zeta(3) - 3840*log(2) + 2230.
Sum_{n>=0} (-1)^n/a(n) = 1490 - 1680*log(2) - 270*zeta(3). (End)
MAPLE
a:=n->(1/360)*(n+1)*(n+2)^3*(n+3)*(2*n+3)*(2*n+5): seq(a(n), n=0..32);
MATHEMATICA
Table[(n + 1)*(n + 2)^3*(n + 3)*(2 n + 3)*(2 n + 5)/360, {n, 0, 25}] (* Amiram Eldar, May 31 2022 *)
CROSSREFS
Sequence in context: A332944 A022681 A266733 * A105249 A278992 A358930
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved