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A308448
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Expansion of Sum_{k>=1} mu(k)*log(1 + x^k/(1 - 2*x^k - x^(2*k)))/k.
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1
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1, 1, 3, 6, 14, 28, 64, 135, 300, 653, 1458, 3223, 7240, 16228, 36678, 83025, 188910, 430730, 985752, 2260866, 5199612, 11982591, 27673826, 64027215, 148399514, 344490100, 800886300, 1864461210, 4346031950, 10142519585, 23696421808, 55420499295, 129742683174, 304014091125
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OFFSET
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1,3
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COMMENTS
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Inverse Euler transform of A000129.
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LINKS
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FORMULA
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-1 + Product_{n>=1} 1/(1 - x^n)^a(n) = g.f. of A000129.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(j-1-a(i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> combinat[fibonacci](n)+b(n, n-1):
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MATHEMATICA
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nmax = 34; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + x^k/(1 - 2 x^k - x^(2 k))]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
nmax = 40; s = ConstantArray[0, nmax]; Do[s[[j]] = j*Fibonacci[j, 2] - Sum[s[[d]]*Fibonacci[j - d, 2], {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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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