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A299113
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Number of rooted identity trees with 2n+1 nodes.
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3
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1, 1, 3, 12, 52, 247, 1226, 6299, 33209, 178618, 976296, 5407384, 30283120, 171196956, 975662480, 5599508648, 32334837886, 187737500013, 1095295264857, 6417886638389, 37752602033079, 222861754454841, 1319834477009635, 7839314017612273, 46688045740233741
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 3:
o o o
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o o o o
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o o o o
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o o o
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o
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MAPLE
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with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(
b(d)*d*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
end:
a:= n-> b(2*n+1):
seq(a(n), n=0..30);
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MATHEMATICA
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b[n_] := b[n] = If[n < 2, n, Sum[b[n - k]*Sum[b[d]*d*(-1)^(k/d + 1), {d, Divisors[k]}], {k, 1, n - 1}]/(n - 1)];
a[n_] := b[2*n + 1];
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PROG
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(Python)
from sympy import divisors
from sympy.core.cache import cacheit
@cacheit
def b(n): return n if n<2 else sum([b(n-k)*sum([b(d)*d*(-1)**(k//d+1) for d in divisors(k)]) for k in range(1, n)])//(n-1)
def a(n): return b(2*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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