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A108681
a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(n+5)*(2*n+3)/720.
0
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).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 18 2005
STATUS
approved