A351403 G.f. A(x) satisfies: (1 - x) = Product_{i>=1, j>=1} A(x^(i*j)).

1, -1, 2, 0, 0, 4, -5, 9, -6, 3, 4, -9, 15, -17, 13, -8, 0, 1, -9, 12, -17, 15, -25, 29, -27, 12, -3, -14, 28, -55, 63, -54, 53, -46, 18, 32, -57, 85, -106, 122, -108, 43, 8, -29, 80, -161, 148, -115, 104, -78, 57, 29, -77, 89, -99, 263, -283, 182, -212, 133, 49

Offset: 0

Author

Ilya Gutkovskiy, Feb 10 2022

Keywords

• sign

Comments

Convolution inverse of A351402.

Crossrefs

Cf. A000005, A007427, A101035, A117208, A288098, A351402.

Programs

Mathematica

nmax = 60; A007427[n_] := Sum[MoebiusMu[d] MoebiusMu[n/d], {d, Divisors[n]}]; CoefficientList[Series[Product[(1 - x^k)^A007427[k], {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f. A(x) satisfies: (1 - x) = Product_{k>=1} A(x^k)^A000005(k).

G.f.: Product_{k>=1} (1 - x^k)^A007427(k).

G.f.: exp( -Sum_{k>=1} A101035(k) * x^k / k ).

a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A101035(k) * a(n-k).