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 A107943 a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)*(2n+3)/8640. 0
 1, 25, 245, 1470, 6468, 22932, 69300, 185130, 448305, 1002001, 2095093, 4140500, 7796880, 14080080, 24511824, 41314284, 67660425, 107991345, 168413245, 257188162, 385334180, 567352500, 822100500, 1173831750, 1653425865 (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. 229). LINKS Table of n, a(n) for n=0..24. Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA G.f.: (1+15*x+40*x^2+25*x^3+3*x^4)/(1-x)^10. - Bruno Berselli, Apr 19 2011 From Amiram Eldar, May 31 2022: (Start) Sum_{n>=0} 1/a(n) = 264*Pi^2 - 49152*log(2)/35 - 57089/35. Sum_{n>=0} (-1)^n/a(n) = 12288*Pi/35 - 12*Pi^2 + 13824*log(2)/35 - 44007/35. (End) MAPLE a:=n->(1/8640)*(n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)*(2*n+3): seq(a(n), n=0..30); MATHEMATICA Table[((n+1)(n+2)^2(n+3)^2(n+4)^2(n+5)(2n+3))/8640, {n, 0, 30}] (* Harvey P. Dale, Apr 19 2011 *) CROSSREFS Sequence in context: A294290 A352304 A362393 * A125388 A126546 A023073 Adjacent sequences: A107940 A107941 A107942 * A107944 A107945 A107946 KEYWORD nonn AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified June 14 04:49 EDT 2024. Contains 373393 sequences. (Running on oeis4.)