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A117211 G.f. A(x) satisfies 1/(1+x) = product_{n>=1} A(x^n). 7

%I

%S 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,

%T -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,

%U -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

%N G.f. A(x) satisfies 1/(1+x) = product_{n>=1} A(x^n).

%C Self-convolution inverse is A117210.

%H Paul D. Hanna, <a href="/A117211/b117211.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: A(x) = exp( -Sum_{n>=1} A117212(n)*x^n/n ).

%F G.f.: A(x) = product_{k>=1}(1 + x^k)^(-mu(k)) where mu(k) is the Möbius function, A008683. - _Stuart Clary_, Apr 15 2006

%t nmax = 88; CoefficientList[ Series[ Product[ (1 + x^k)^(-MoebiusMu[k]), {k, 1, nmax} ], {x, 0, nmax} ], x ] (* _Stuart Clary_, Apr 15 2006 *)

%o (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)))}

%Y Cf. A117212 (l.g.f.), A117210 (inverse); variants: A117208, A117209.

%K sign

%O 0,3

%A _Paul D. Hanna_, Mar 03 2006

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)