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A290362
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Number of 8-leaf rooted trees with n levels.
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2
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0, 1, 22, 223, 1344, 5727, 19193, 54046, 133476, 297633, 611644, 1175845, 2138500, 3711279, 6187767, 9965276, 15570232, 23687409, 35193282, 51193771, 73066648, 102508879, 141589173, 192806010, 259151420, 344180785, 452088936, 587792817, 757020988, 966410239
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OFFSET
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0,3
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LINKS
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B. A. Huberman and T. Hogg, Complexity and adaptation, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.
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FORMULA
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G.f.: (5*x^5+57*x^4+120*x^3+75*x^2+14*x+1)*x / (x-1)^8.
a(n) = (272*n^7+273*n^6+749*n^5+1365*n^4+1043*n^3+882*n^2+456*n)/7!.
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MAPLE
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a:= n-> ((((((272*n+273)*n+749)*n+1365)*n+1043)*n+882)*n+456)*n/7!:
seq(a(n), n=0..40);
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MATHEMATICA
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LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 1, 22, 223, 1344, 5727, 19193, 54046}, 30] (* Harvey P. Dale, Oct 16 2017 *)
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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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STATUS
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approved
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