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Search: id:A117211
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| A117211 |
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G.f. A(x) satisfies: 1/(1+x) = product_{n>=1} A(x^n). |
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+0
6
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| 1, -1, 2, -1, 1, 1, -2, 4, -4, 4, -3, 2, 0, -1, 2, -3, 4, -5, 5, -4, 4, -3, 1, 1, -2, 3, -5, 5, -5, 3, -1, 1, 3, -4, 3, -2, 2, -1, -3, 4, -6, 4, -4, 5, 0, -4, 2, -1, 4, -2, 3, -3, 6, -9, 7, -1, 1, -4, -8, 10, -6, 10, -11, 12, -9, -4, 7, -7, 15, -25, 10, -5, 13, 1, -6, 16, -21, 14, -15, 28, -6, -12, -3, 1, 18, -18, 17, -25, 13
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Self-convolution inverse is A117210.
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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
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MATHEMATICA
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nmax = 88; 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, (-1)^n-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.), A117210 (inverse); variants: A117208, A117209.
Sequence in context: A026519 A025177 A026148 this_sequence A061545 A126886 A105685
Adjacent sequences: A117208 A117209 A117210 this_sequence A117212 A117213 A117214
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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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