A107970 a(n) = (n+1)*(n+2)^3*(n+3)*(2n+3)*(2n+5)/360.

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).

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

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

Adjacent sequences: A107967 A107968 A107969 * A107971 A107972 A107973

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved