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URL: https://oeis.org/A307648

⇱ A307648 - OEIS

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A307648
G.f. A(x) satisfies: 1/(1 - x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...
3
1, 1, -1, -4, -3, -2, 7, 7, 4, -6, 14, -11, -4, -47, 9, 6, 161, -93, -33, -269, 232, -83, 660, -733, 500, -779, 1527, -2291, 1876, -3892, 5598, -3056, 7791, -14088, 11289, -17113, 28083, -26211, 34645, -60715, 73180, -80951, 111926, -155269, 178561, -233709, 359679, -403884, 454659, -697310, 862133
OFFSET
0,4
COMMENTS
Euler transform of A055615.
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^(mu(k)*k).
G.f.: exp(Sum_{k>=1} A046970(k)*x^k/k).
EXAMPLE
G.f.: A(x) = 1 + x - x^2 - 4*x^3 - 3*x^4 - 2*x^5 + 7*x^6 + 7*x^7 + 4*x^8 - 6*x^9 + 14*x^10 - 11*x^11 - 4*x^12 - 47*x^13 + ...
MATHEMATICA
terms = 50; CoefficientList[Series[Product[1/(1 - x^k)^(MoebiusMu[k] k), {k, 1, terms}], {x, 0, terms}], x]
terms = 50; CoefficientList[Series[Exp[Sum[Sum[MoebiusMu[d] d^2, {d, Divisors[k]}] x^k/k, {k, 1, terms}]], {x, 0, terms}], x]
terms = 50; A[_] = 1; Do[A[x_] = 1/((1 - x) Product[A[x^k]^k, {k, 2, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 19 2019
STATUS
approved