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Search: id:A159595
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| A159595 |
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G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(k,n)*x^k ]^n/n ). |
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+0
2
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| 1, 1, 4, 13, 56, 286, 2008, 19749, 280842, 5762129, 168873970, 7023348917, 412682000624, 34188301513404, 3992802803844526, 656649238572375132, 152278229304524217542, 49749953321847000835094
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Define sigma(k,n) = Sum_{d|k} d^n.
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 13*x^3 + 56*x^4 + 286*x^5 + 2008*x^6 +...
log(A(x)) = Sum_{n>=1} [x + sigma(2,n)*x^2 + sigma(3,n)*x^3 +...]^n/n.
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=1, n, sigma(k, m)*x^k+x*O(x^n))^m/m))); polcoeff(A, n)}
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CROSSREFS
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Sequence in context: A121076 A121070 A163070 this_sequence A009300 A149477 A149478
Adjacent sequences: A159592 A159593 A159594 this_sequence A159596 A159597 A159598
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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), May 05 2009
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