A108681 a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(n+5)*(2*n+3)/720.

1, 15, 98, 420, 1386, 3822, 9240, 20196, 40755, 77077, 138138, 236600, 389844, 621180, 961248, 1449624, 2136645, 3085467, 4374370, 6099324, 8376830, 11347050, 15177240, 20065500, 26244855, 33987681, 43610490, 55479088, 70014120, 87697016, 109076352, 134774640

Offset: 0

Author

Emeric Deutsch, Jun 18 2005

Keywords

• nonn
• easy

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. 232, # 4).

Links

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

Programs

Maple

G:=factor(sum(a(n)*z^n,n=0..infinity)); series(G,z=0,37);

Mathematica

Table[(n+1)(n+2)^2(n+3)(n+4)(n+5)(2n+3)/720,{n,0,30}] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,15,98,420,1386,3822,9240,20196},30] (* Harvey P. Dale, Sep 23 2017 *)

Formula

G.f.: (1+x)*(1+6*x)/(1-x)^8.

From Amiram Eldar, Jun 02 2022: (Start)

Sum_{n>=0} 1/a(n) = 20*Pi^2 - 3072*log(2)/7 + 4531/42.

Sum_{n>=0} (-1)^n/a(n) = 768*Pi/7 - 10*Pi^2 - 256*log(2)/7 - 9227/42. (End)

a(n) = A027818(n)+A027818(n-1). - R. J. Mathar, Jul 22 2022