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A339642
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Number of rooted trees with n nodes colored using exactly 2 colors.
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3
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0, 2, 10, 44, 196, 876, 4020, 18766, 89322, 431758, 2116220, 10494080, 52569504, 265647586, 1352621168, 6933127446, 35745747902, 185256755454, 964575991660, 5043194697556, 26467075595080, 139375175511598, 736228488297566, 3900073083063348, 20714052518640904
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 10 includes 5 trees and their color complements:
(1(12)), (1(22)), (1(1(2))), (1(2(1))), (1(2(2))).
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MAPLE
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b:= proc(n, k) option remember; `if`(n<2, k*n, (add(add(b(d, k)*
d, d=numtheory[divisors](j))*b(n-j, k), j=1..n-1))/(n-1))
end:
a:= n-> b(n, 2)-2*b(n, 1):
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n < 2, k*n, (Sum[Sum[b[d, k]*d, {d, Divisors[j]}]*b[n - j, k], {j, 1, n - 1}])/(n - 1)];
a[n_] := b[n, 2] - 2*b[n, 1];
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PROG
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seq(n)={U(n, 2) - 2*U(n, 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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