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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 (list; graph; refs; listen; history; text; internal format)
 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 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. 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 A307158 Adjacent sequences:  A108678 A108679 A108680 * A108682 A108683 A108684 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 18 2005 STATUS approved

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)