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

0,2

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. 232, # 4).

Links

Table of n, a(n) for n=0..31.

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

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

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 *)

Crossrefs

Sequence in context: A232296 A278203 A159528 * A108254 A174383 A341396

Adjacent sequences: A108678 A108679 A108680 * A108682 A108683 A108684

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 18 2005

Status

approved