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A319668 Expansion of Product_{k>=1} (1 - x^k - x^(2*k)). 1
1, -1, -2, 0, 0, 3, 1, 3, 1, -2, 0, -3, -6, -4, 1, -8, 1, 2, 5, 5, 4, 9, 13, 7, 3, 1, 3, 7, -16, -9, -17, -13, -21, -5, -25, -33, -3, -3, -9, 22, -6, 11, 29, 29, 57, 37, 40, 31, 58, 18, 35, 40, 37, -24, -36, -34, -29, -60, -54, -98, -74, -124, -113, -156, -71, -35, -140, -46, -16, -61, -25 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..70.

FORMULA

G.f.: exp(Sum_{k>=1} Sum_{j>=1} phi(j)*log(1 - x^(j*k)*(1 + x^(j*k)))/(j*k)), where phi = Euler totient function (A000010).

MAPLE

a:=series(mul((1-x^k-x^(2*k)), k=1..100), x=0, 71): seq(coeff(a, x, n), n=0..70); # Paolo P. Lava, Apr 02 2019

MATHEMATICA

nmax = 70; CoefficientList[Series[Product[(1 - x^k - x^(2 k)), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 70; CoefficientList[Series[Exp[Sum[Sum[EulerPhi[j] Log[1 - x^(j k) (1 + x^(j k))]/(j k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, -Sum[Sum[Sum[EulerPhi[d/j] (Fibonacci[j - 1] + Fibonacci[j + 1]), {j, Divisors[d]}], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 70}]

CROSSREFS

Cf. A000010, A000358, A000726, A109389, A137569, A162891, A263401.

Sequence in context: A131636 A188023 A077888 * A167634 A174169 A248174

Adjacent sequences:  A319665 A319666 A319667 * A319669 A319670 A319671

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Sep 25 2018

STATUS

approved

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Last modified March 28 11:49 EDT 2020. Contains 333083 sequences. (Running on oeis4.)