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A163203
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G.f.: exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d^n] * x^n/n ).
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2
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1, 1, 2, 11, 79, 713, 8486, 127372, 2248390, 45527161, 1048442107, 27060812167, 771886991408, 24110090108332, 818871809076474, 30044771201925569, 1184069354974499199, 49884064948928968400, 2237283630465903060711
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OFFSET
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0,3
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COMMENTS
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A variant of A023881, which is defined by g.f.:
exp( Sum_{n>=1} [Sum_{d|n} d^n] * x^n/n )
where A023881 is the number of partitions in expanding space.
Compare also to the g.f. of A006950 given by:
exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d] * x^n/n ),
where A006950(n) is the number of partitions of n in which each even part occurs with even multiplicity.
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LINKS
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FORMULA
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a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-1)/2 + 2*exp(-2))/n^2). - Vaclav Kotesovec, Aug 17 2015
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EXAMPLE
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G.f.: 1 + x + 2*x^2 + 11*x^3 + 79*x^4 + 713*x^5 + 8486*x^6 +...
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, (-1)^(m-d)*d^m)*x^m/m)+x*O(x^n)), n)}
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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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