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

0,3

Comments

Self-convolution inverse is A117210.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

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

Mathematica

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

Prog

(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)))}

Crossrefs

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

Sequence in context: A026519 A025177 A026148 * A246576 A358273 A215894

Adjacent sequences: A117208 A117209 A117210 * A117212 A117213 A117214

Keyword

sign

Author

Paul D. Hanna, Mar 03 2006

Status

approved