A028343 - OEIS

A028343

Expansion of Product_{i>=1} (1-x^i)^(1/i); also of exp(- Sum_{n>=1}(d(n)*x^n/n)) where d(n) is the number of divisors of n.

1, -1, -1, 1, -1, 41, -131, 1499, -4159, 10639, 100871, 4142249, -111459041, 1127459321, 1797229589, -185028952109, 706529394689, 29136228245279, -547852336663409, 7139784702100049, -195178627579232449

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OFFSET

0,6

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..445

FORMULA

E.g.f.: Product_{i>=1} (1-x^i)^(1/i).

EXAMPLE

G.f. = 1 - x - x^2 + x^3 - x^4 + 41*x^5 - 131*x^6 + 1499*x^7 - 4159*x^8 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 - x^k)^(1/k), {k, 1, nmax}], {x, 0, nmax}], x]*Range[0, nmax]! (* G. C. Greubel, Nov 24 2016 *)

a[ n_] := If[n < 0, 0, n! SeriesCoefficient[ Exp[ -Sum[DivisorSigma[0, k] x^k/k, {k, n}]], {x, 0, n}]]; (* Michael Somos, Nov 25 2016 *)

CROSSREFS

Sequence in context: A142290 A013643 A142333 * A165816 A325069 A321890

Adjacent sequences: A028340 A028341 A028342 * A028344 A028345 A028346

KEYWORD

sign

AUTHOR

Jeffrey Shallit

STATUS

approved