A320786 Inverse Euler transform of {1,0,1,0,0,0,...}

1, 1, -1, 1, -1, 1, -2, 2, -2, 3, -5, 6, -7, 11, -16, 20, -27, 39, -55, 75, -102, 145, -207, 286, -397, 565, -802, 1123, -1581, 2248, -3193, 4517, -6399, 9112, -12984, 18457, -26270, 37502, -53553, 76416, -109146, 156135, -223446, 319764, -457884, 656288, -941081

Offset

0,7

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). The constant term 1 is sometimes taken to be the zeroth part of the Euler transform.

Links

Table of n, a(n) for n=0..46.

OEIS Wiki, Euler transform

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[PadRight[{1, 0, 1}, 50]]

Crossrefs

Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054.

Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549.

Inverse Euler transforms: A059966, A320767, A320776, A320777, A320778, A320779, A320780, A320781, A320782.

Sequence in context: A365615 A278167 A239470 * A126111 A100142 A296103

Adjacent sequences: A320783 A320784 A320785 * A320787 A320788 A320789

Keyword

sign

Author

Gus Wiseman, Oct 22 2018

Status

approved