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A167066
Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 5}, {4, 5}}.
1
24, 20160, 14515200, 10373448960, 7410329640120, 5293465841664000, 3781306797401609112, 2701118650243184317440, 1929502759140378901785600, 1378310758353447731649144000, 984575190426384431371033497336, 703316214957312006365562863616000, 502403171470887016026721609133115192
OFFSET
1,1
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
FORMULA
a(n) = 840 a(n-1)
- 95522 a(n-2)
+ 4231920 a(n-3)
- 87627601 a(n-4)
+ 863951760 a(n-5)
- 3862082882 a(n-6)
+ 9004563960 a(n-7)
- 11846119204 a(n-8)
+ 9004563960 a(n-9)
- 3862082882 a(n-10)
+ 863951760 a(n-11)
- 87627601 a(n-12)
+ 4231920 a(n-13)
- 95522 a(n-14)
+ 840 a(n-15)
- a(n-16)
G.f.: -24x(x^14 -5278x^12 +201600x^11 -2458194x^10 +8663760x^9 -10786195x^8 +10786195x^6 -8663760x^5 +2458194x^4 -201600x^3 +5278x^2 -1)/ (x^16 -840x^15 +95522x^14 -4231920x^13 +87627601x^12 -863951760x^11 +3862082882x^10 -9004563960x^9 +11846119204x^8 -9004563960x^7 +3862082882x^6 -863951760x^5 +87627601x^4 -4231920x^3 +95522x^2 -840x +1).
CROSSREFS
Sequence in context: A279655 A067746 A111404 * A166338 A258874 A188961
KEYWORD
nonn
AUTHOR
STATUS
approved