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A329274
Expansion of 1 / (1 + Sum_{k>=1} phi(k) * log(1 - 2 * x^k) / k), where phi = A000010.
0
1, 2, 7, 24, 83, 286, 989, 3416, 11807, 40806, 141041, 487488, 1684971, 5823986, 20130299, 69579356, 240497727, 831269134, 2873243541, 9931234972, 34326861907, 118649239730, 410105717339, 1417511828340, 4899565424887, 16935125993974, 58535496103303, 202325291692972
OFFSET
0,2
COMMENTS
Invert transform of A000031.
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A000031(k) * a(n-k).
MATHEMATICA
nmax = 27; CoefficientList[Series[1/(1 + Sum[EulerPhi[k] Log[1 - 2 x^k]/k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[(1/k) DivisorSum[k, EulerPhi[#] 2^(k/#) &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 27}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 11 2019
STATUS
approved