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A320767 Inverse Euler transform applied once to {1,-1,0,0,0,...}, twice to {1,0,0,0,0,...}, or three times to {1,1,1,1,1,...}. 9
1, 1, -2, 1, -1, 2, -3, 4, -5, 8, -13, 18, -25, 40, -62, 90, -135, 210, -324, 492, -750, 1164, -1809, 2786, -4305, 6710, -10460, 16264, -25350, 39650, -62057, 97108, -152145, 238818, -375165, 589520, -927200, 1459960, -2300346, 3626200, -5720274, 9030450 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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
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]}]];
Nest[EulerInvTransform, Array[DiscreteDelta, 50, 0], 2]
CROSSREFS
Sequence in context: A022910 A030737 A238587 * A058713 A331564 A288250
KEYWORD
sign
AUTHOR
Gus Wiseman, Oct 20 2018
STATUS
approved

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Last modified February 21 04:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)