A353927 Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} mu(n)*x^n, where mu = A008683.

1, -1, 0, -1, -1, 2, -4, 4, -7, 8, -10, 9, -5, -6, 19, -40, 70, -110, 138, -158, 154, -93, -70, 355, -797, 1408, -2160, 2925, -3479, 3399, -2080, -1299, 7593, -17673, 32014, -49928, 68683, -82847, 82807, -53620, -24942, 176293, -422887, 777264, -1226688, 1710686, -2093347

Offset

1,6

Comments

Inverse weigh transform of the Moebius function (A008683).

Links

Table of n, a(n) for n=1..47.

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = MoebiusMu[n] - b[n, n - 1]; Table[a[n], {n, 1, 47}]

Crossrefs

Cf. A008683, A320781, A353926.

Sequence in context: A272881 A325646 A325723 * A262884 A340448 A241387

Adjacent sequences: A353924 A353925 A353926 * A353928 A353929 A353930

Keyword

sign

Author

Ilya Gutkovskiy, May 11 2022

Status

approved