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A167059
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Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}}.
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1
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8, 4032, 1612800, 631427328, 246562692200, 96244833484800, 37566939748080392, 14663279200231130112, 5723424260979717196800, 2233987356983360324068800, 871977888467614764819315368, 340353508793721676084268236800, 132847991246505889127220947758952
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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 A X P_n, Ars Combin. 49 (1998), 129-154.
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LINKS
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P. Raff, Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}}. Contains sequence, recurrence, generating function, and more.
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FORMULA
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a(n) = 504 a(n-1)
- 48706 a(n-2)
+ 1765008 a(n-3)
- 29021617 a(n-4)
+ 239655024 a(n-5)
- 1039298722 a(n-6)
+ 2447629128 a(n-7)
- 3242171236 a(n-8)
+ 2447629128 a(n-9)
- 1039298722 a(n-10)
+ 239655024 a(n-11)
- 29021617 a(n-12)
+ 1765008 a(n-13)
- 48706 a(n-14)
+ 504 a(n-15)
- a(n-16)
G.f.: -8x (x^14 -3710x^12 +104832x^11 -997954x^10 +3633840x^9 -4759203x^8 +4759203x^6 -3633840x^5 +997954x^4 -104832x^3 +3710x^2-1)/ (x^16 -504x^15 +48706x^14 -1765008x^13 +29021617x^12 -239655024x^11 +1039298722x^10 -2447629128x^9 +3242171236x^8 -2447629128x^7 +1039298722x^6 -239655024x^5 +29021617x^4 -1765008x^3 +48706x^2 -504x+1).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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