A320781 Inverse Euler transform of the Moebius function A008683.

1, -2, 0, 0, -1, 2, -4, 5, -7, 9, -10, 7, -5, -2, 19, -44, 70, -103, 138, -166, 154, -83, -70, 346, -797, 1413, -2160, 2931, -3479, 3380, -2080, -1259, 7593, -17743, 32014, -49818, 68683, -82985, 82807, -53462, -24942, 176139, -422887, 777357, -1226688

Offset

1,2

Comments

The Euler transform of a sequence q is the sequence of coefficients of x^n, n > 0, in the expansion of Product_{n > 0} 1/(1 - x^n)^q(n).

Links

Table of n, a(n) for n=1..45.

OEIS Wiki, Euler transform

Maple

# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(n -> ifelse(n=0, 1, NumberTheory:-Moebius(n))):
seq(a(n), n = 1..45); # Peter Luschny, Nov 21 2022

Mathematica

EulerInvTransform[{}]={}; EulerInvTransform[seq_]:=Module[{final={}}, For[i=1, i<=Length[seq], i++, AppendTo[final, i*seq[[i]]-Sum[final[[d]]*seq[[i-d]], {d, i-1}]]];
Table[Sum[MoebiusMu[i/d]*final[[d]], {d, Divisors[i]}]/i, {i, Length[seq]}]];
EulerInvTransform[Table[MoebiusMu[n], {n, 30}]]

Crossrefs

Sequence in context: A051510 A361800 A340958 * A284608 A325201 A260019

Adjacent sequences: A320778 A320779 A320780 * A320782 A320783 A320784

Keyword

sign

Author

Gus Wiseman, Oct 22 2018

Status

approved