A117210 G.f. A(x) satisfies (1+x) = product_{n>=1} A(x^n).

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, -2, -2, 5, -1, 3, -6, 2, 0, 11, -6, -4, -10, 12, -1, 6, -13, 5, -8, 16, -8, 9, -13, 17, -17, 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

Offset

0,4

Comments

Self-convolution inverse is A117211.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Paul D. Hanna)

N. J. A. Sloane, Transforms

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

Weigh transform of A008683(n). - Vladeta Jovovic, Apr 20 2006

Mathematica

nmax = 81; 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, -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.), A117211 (inverse); variants: A117208, A117209.

Sequence in context: A117163 A096863 A326815 * A060277 A333330 A290825

Adjacent sequences: A117207 A117208 A117209 * A117211 A117212 A117213

Keyword

sign,look

Author

Paul D. Hanna, Mar 03 2006

Status

approved