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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
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
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.)