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A328774 Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} phi(n) * x^n, where phi = A000010. 0
1, 1, 1, 1, 2, -2, 4, -3, 4, -7, 14, -21, 30, -38, 50, -79, 128, -190, 286, -419, 598, -895, 1386, -2121, 3178, -4733, 7122, -10796, 16414, -25011, 38056, -57722, 87568, -133308, 203618, -311318, 475536, -726069, 1109718, -1698185, 2601166, -3987305, 6114666, -9378656, 14389676 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Inverse weigh transform of A000010.

LINKS

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

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= proc(n) option remember; numtheory[phi](n)-b(n, n-1) end:

seq(a(n), n=1..45);  # Alois P. Heinz, Oct 27 2019

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] = EulerPhi[n] - b[n, n - 1]; Array[a, 45]

CROSSREFS

Cf. A000010, A299069, A320778.

Sequence in context: A233574 A157927 A227256 * A131816 A223541 A128181

Adjacent sequences:  A328771 A328772 A328773 * A328775 A328776 A328777

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Oct 27 2019

STATUS

approved

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Last modified September 23 08:23 EDT 2021. Contains 347610 sequences. (Running on oeis4.)