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Search: id:A117210
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| A117210 |
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G.f. A(x) satisfies: (1+x) = product_{n>=1} A(x^n). |
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+0
6
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| 1, 1, -1, -2, 0, 1, 1, 0, -1, -1, 2, 1, -2, -3, 2, 4, 2, -5, -4, 0, 5, 2, 1, -5, -1, 2, 5, -5, -2, -2, 5, -1, 3, -6, 2, 0, 11, -6, -4, -10, 12, -1, 6, -13, 5, -8, 16, -8, 9, -13, 17, -17, 7, -21, 25, -10, 22, -29, 20, -24, 34, -24, 27, -44, 35, -32, 39, -52, 45, -39, 66, -53, 47, -76, 70, -55, 79, -98, 66, -84, 115, -89
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Self-convolution inverse is A117211.
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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G.f.: A(x) = exp( Sum_{n>=1} A117212(n)*x^n/n ).
G.f.: A(x) = product_{k>=1}(1 + x^k)^mu(k) where mu(k) is the Moebius (Mobius) function, A008683 - Stuart Clary (clary(AT)uakron.edu), Apr 15, 2006
Weigh transform of A008683(n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 20 2006
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MATHEMATICA
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nmax = 81; CoefficientList[ Series[ Product[ (1 + x^k)^(MoebiusMu[k]), {k, 1, nmax} ], {x, 0, nmax} ], x ] - Stuart Clary (clary(AT)uakron.edu), Apr 15, 2006
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, if(n==1, 1, -polcoeff(prod(i=1, n, sum(k=0, min(n\i, n-1), a(k)*x^(i*k))+x*O(x^n)), n, x)))}
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CROSSREFS
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Cf. A117212 (log.g.f.), A117211 (inverse); variants: A117208, A117209.
Sequence in context: A054845 A117163 A096863 this_sequence A060277 A101672 A083731
Adjacent sequences: A117207 A117208 A117209 this_sequence A117211 A117212 A117213
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 03 2006
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