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A308447
Expansion of Sum_{k>=1} mu(k)*log(1 + x^k/((1 - x^k)*(1 - 2*x^k)))/k.
1
1, 2, 4, 5, 8, 8, 16, 25, 52, 98, 192, 345, 640, 1162, 2164, 4050, 7680, 14534, 27648, 52479, 99956, 190554, 364544, 698525, 1341848, 2580790, 4971616, 9587565, 18513920, 35790276, 69271552, 134211600, 260297012, 505286430, 981714296, 1908881520, 3714580480, 7233615306
OFFSET
1,2
COMMENTS
Inverse Euler transform of A000225.
LINKS
FORMULA
-1 + Product_{n>=1} 1/(1 - x^n)^a(n) = g.f. of A000225.
a(n) ~ 2^n/n. - Vaclav Kotesovec, May 28 2019
MATHEMATICA
nmax = 38; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + x^k/((1 - x^k) (1 - 2 x^k))]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
nmax = 50; s = ConstantArray[0, nmax]; Do[s[[j]] = j*(2^ j - 1) - Sum[s[[d]]*(2^(j - d) - 1), {d, 1, j - 1}], {j, 1, nmax}]; Table[Sum[MoebiusMu[k/d]*s[[d]], {d, Divisors[k]}]/k, {k, 1, nmax}] (* Vaclav Kotesovec, Aug 10 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 27 2019
STATUS
approved