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A168243
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Expansion of e.g.f. Product_{i>=1} (1 + x^i)^(1/i).
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21
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1, 1, 1, 5, 11, 59, 439, 2659, 13705, 160649, 2009681, 16966421, 183312931, 2078169235, 34203787591, 657685416179, 8054585463569, 104530824746129, 2595754682459425, 39767021562661669, 758079429084897211
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: exp(Sum_{n>=1} A048272(n)*x^n/n).
Conjecture: log(a(n)/n!) ~ (log(2) - 1) * log(n). - Vaclav Kotesovec, Sep 10 2018
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MATHEMATICA
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nmax=20; CoefficientList[Series[Product[(1+x^k)^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 28 2015 *)
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[-(-1)^d, {d, Divisors[k]}]*a[n-k], {k, 1, n}]/n]; Table[n!*a[n], {n, 0, 20}] (* Vaclav Kotesovec, Sep 07 2018 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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