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Search: id:A163203
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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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+0
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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COMMENT
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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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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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PROGRAM
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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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Cf. A023881, A006950, A002129.
Sequence in context: A094569 A151418 A154273 this_sequence A142722 A099661 A027110
Adjacent sequences: A163200 A163201 A163202 this_sequence A163204 A163205 A163206
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 22 2009
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