|
%I #20 Mar 25 2018 06:42:47
%S 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,
%T -2,-2,5,-1,3,-6,2,0,11,-6,-4,-10,12,-1,6,-13,5,-8,16,-8,9,-13,17,-17,
%U 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
%N G.f. A(x) satisfies (1+x) = product_{n>=1} A(x^n).
%C Self-convolution inverse is A117211.
%H Vaclav Kotesovec, <a href="/A117210/b117210.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Paul D. Hanna)
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</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
%F Weigh transform of A008683(n). - _Vladeta Jovovic_, Apr 20 2006
%t nmax = 81; 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, -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.), A117211 (inverse); variants: A117208, A117209.
%K sign,look
%O 0,4
%A _Paul D. Hanna_, Mar 03 2006
|
