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A060905
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Expansion of e.g.f. exp(x*exp(x) + 1/2*x^2*exp(x)^2).
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12
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1, 1, 4, 19, 110, 751, 5902, 52165, 509588, 5437729, 62828306, 780287839, 10351912276, 145944541159, 2176931651546, 34225419288421, 565282627986368, 9779830102138945, 176776613812205074, 3330780287838743575
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OFFSET
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0,3
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COMMENTS
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Number of functions f from a set of size n to itself such that f(f(f(x))) = f(x). - Joel B. Lewis, Dec 12 2011
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
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LINKS
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FORMULA
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E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 1, m = 2.
a(n) = sum(sum(k^(n-k)/(n-k)!*binomial(m,k-m)*(1/2)^(k-m),k,m,n)/m!,m,1,n), n>0. - Vladimir Kruchinin, Aug 20 2010
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MATHEMATICA
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nn=20; a=x Exp[x]; Range[0, nn]!CoefficientList[Series[Exp[a+a^2/2], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 18 2012 *)
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PROG
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(Maxima) a(n):=sum(sum(k^(n-k)/(n-k)!*binomial(m, k-m)*(1/2)^(k-m), k, m, n)/m!, m, 1, n); [Vladimir Kruchinin, Aug 20 2010]
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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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