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A130907
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E.g.f.: exp(x+x^2/2)/(1-x).
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2
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1, 2, 6, 22, 98, 516, 3172, 22436, 180252, 1624888, 16258376, 178877832, 2146674136, 27907332272, 390705042288, 5860585983856, 93769421948432, 1594080384922656, 28693447925921632
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internal format)
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OFFSET
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0,2
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COMMENTS
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A jeweler creates collections of necklaces using exactly n different colored beads ( to make the entire collection) then chooses some (or none or all) of the necklaces to sell. [From Geoffrey Critzer, Apr 20 2009]
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LINKS
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FORMULA
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a(n)=n!+(sum(m=0..n, sum(k=1..m, (binomial(k,m-k)*2^(k-m))/k!)))*n!. [From Vladimir Kruchinin, Jul 02 2011]
D-finite with recurrence a(n) = (n+1)*a(n-1) - (n-2)*(n-1)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012
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MATHEMATICA
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CoefficientList[Series[Exp[x + x^2/2 - Log[1 - x]], {x, 0, 20}], x]* Table[n!, {n, 0, 20}] [From Geoffrey Critzer, Apr 20 2009]
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PROG
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(PARI) x='x+O('x^66); /* that many terms */
egf=exp(x+x^2/2)/(1-x);
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Jul 11 2011 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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