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A320783
Inverse Euler transform of (-1)^(n - 1).
0
1, 1, -2, 2, -3, 6, -11, 18, -30, 56, -105, 186, -335, 630, -1179, 2182, -4080, 7710, -14588, 27594, -52377, 99858, -190743, 364722, -698870, 1342176, -2581425, 4971008, -9586395, 18512790, -35792449, 69273666, -134215680, 260300986, -505294125, 981706806
OFFSET
0,3
COMMENTS
After a(1) and a(2), same as A038063.
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.
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[Array[(-1)^(#-1)&, 30]]
CROSSREFS
Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054.
Inverse Euler transforms: A059966, A320767, A320776, A320777, A320778, A320779, A320780, A320781, A320782.
Sequence in context: A185084 A145778 A102762 * A049853 A162599 A064319
KEYWORD
sign
AUTHOR
Gus Wiseman, Oct 22 2018
STATUS
approved