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A309994
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Number of forests of rooted trees with 2n colored nodes using exactly n colors.
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2
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1, 2, 89, 14845, 5613775, 3809941836, 4073969863427, 6316651717425358, 13407079935176225215, 37344967651943608528498, 132181958309965092862822183, 579566807739313784043087337938, 3083812115454145185391757131500066, 19577110356940490275990571617295644659
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OFFSET
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0,2
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, k) option remember; `if`(n<2, n, (add(add(d*b(d, k),
d=numtheory[divisors](j))*b(n-j, k)*k, j=1..n-1))/(n-1))
end:
a:= n-> add(b(2*n+1, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..15);
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n < 2, n, Sum[Sum[d*b[d, k], {d, Divisors[j]}]*b[n-j, k]*k, {j, 1, n-1}]/(n-1)];
a[n_] := Sum[b[2*n+1, n-i]*(-1)^i*Binomial[n, i], {i, 0, n}];
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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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