A117211 G.f. A(x) satisfies 1/(1+x) = product_{n>=1} A(x^n).
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
Offset: 0
Keywords
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
nmax = 88; CoefficientList[ Series[ Product[ (1 + x^k)^(-MoebiusMu[k]), {k, 1, nmax} ], {x, 0, nmax} ], x ] (* Stuart Clary, Apr 15 2006 *) -
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)))}
Formula
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 Möbius function, A008683. - Stuart Clary, Apr 15 2006
Comments