A280197 Expansion of 1/(1 - Sum_{k>=2} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683).

1, 0, 1, 1, 1, 3, 3, 6, 8, 12, 20, 28, 45, 68, 102, 159, 238, 367, 557, 849, 1298, 1973, 3015, 4592, 7002, 10679, 16276, 24822, 37841, 57696, 87971, 134119, 204497, 311783, 475370, 724786, 1105053, 1684853, 2568837, 3916642, 5971587, 9104711, 13881698, 21165024, 32269721, 49200718, 75014949, 114373158, 174381511

Offset: 0

Author

Ilya Gutkovskiy, Dec 28 2016

Keywords

• nonn

Comments

Number of compositions (ordered partitions) into squarefree parts > 1 (A144338).

Examples

			a(5) = 3 because we have [5], [3, 2] and [2, 3].
		

Links

• Robert Israel, Table of n, a(n) for n = 0..5456
• Eric Weisstein's World of Mathematics, Squarefree
• Index entries for sequences related to compositions

Crossrefs

Cf. A005117, A008683, A073576, A144338, A280127, A280194.

Programs

Maple

N:= 100: # for a(0)..a(N)
g:= 1/(1-add(numtheory:-mobius(k)^2*x^k, k=2..N)):
S:= series(g,x,N+1):
seq(coeff(S,x,j),j=0..N); # Robert Israel, Dec 29 2016

Mathematica

nmax = 48; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=2} mu(k)^2*x^k).