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A038075
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Number of rooted identity trees with 2-colored leaves.
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7
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2, 2, 3, 7, 16, 41, 110, 304, 858, 2474, 7234, 21418, 64057, 193277, 587531, 1797817, 5532916, 17115442, 53186682, 165958893, 519764706, 1633331926, 5148420607, 16273962742, 51574291758, 163834983761, 521597902077, 1663993969029, 5318540288800, 17029516243797
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OFFSET
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1,1
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LINKS
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FORMULA
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Shifts left under Weigh transform.
a(n) ~ c * d^n / n^(3/2), where d = 3.3683668081969694736300401764..., c = 0.4229796097587478606873477... . - Vaclav Kotesovec, Sep 10 2014
G.f. A(x) satisfies: A(x) = x + x * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) / k ). - Ilya Gutkovskiy, May 19 2023
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> `if`(n<2, 2*n, b(n-1, n-1)):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n- i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n<2, 2*n, b[n-1, 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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