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A003750
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Number of Hamiltonian paths in K_5 X P_n.
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1
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60, 8760, 617400, 36021240, 1871009400, 90539967480, 4181860331640, 187073020183800, 8181829090755960, 352081040138505720, 14972983484769861240, 631272829225942738680, 26446059244840564688760, 1102721870861189212971000, 45821243162927769017364600
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OFFSET
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1,1
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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
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LINKS
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FORMULA
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a(1) = 60,
a(2) = 8760,
a(3) = 617400,
a(4) = 36021240,
a(5) = 1871009400,
a(6) = 90539967480,
a(7) = 4181860331640,
a(8) = 187073020183800, and
a(n) = 95a(n-1) - 2854a(n-2) + 23880a(n-3) + 97152a(n-4) + 29616a(n-5) - 19296a(n-6) - 6912a(n-7).
G.f.: 60*x*(6912*x^7 -48096*x^6 +39216*x^5 -66112*x^4 +15608*x^3 -726*x^2 +51*x +1)/((12*x^2 +28*x-1)^2*(48*x^3 -90*x^2 -39*x +1)). - Colin Barker, Aug 30 2012
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MATHEMATICA
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CoefficientList[Series[60 (6912 x^7 - 48096 x^6 + 39216 x^5 - 66112 x^4 + 15608 x^3 - 726 x^2 + 51 x + 1)/((12 x^2 + 28 x - 1)^2 (48 x^3 - 90 x^2 - 39 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)
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PROG
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(PARI) Vec(60*x*(6912*x^7-48096*x^6+39216*x^5-66112*x^4+15608*x^3-726*x^2+51*x+1)/((12*x^2+28*x-1)^2*(48*x^3-90*x^2-39*x+1))+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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