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A363062
G.f. A(x) satisfies: A(x) = x - x^2 * exp(A(x) + A(x^2)/2 + A(x^3)/3 + A(x^4)/4 + ...).
1
1, -1, -1, 0, 1, 1, -1, -2, 0, 4, 4, -5, -13, -2, 26, 30, -29, -94, -26, 189, 246, -198, -769, -302, 1512, 2228, -1372, -6691, -3425, 12672, 21046, -9503, -60776, -38353, 109719, 205330, -61001, -567518, -427145, 967914, 2045196, -314417, -5405209, -4743873, 8625547
OFFSET
1,8
FORMULA
G.f.: x - x^2 / Product_{n>=1} (1 - x^n)^a(n).
a(1) = 1, a(2) = -1; a(n) = (1/(n - 2)) * Sum_{k=1..n-2} ( Sum_{d|k} d * a(d) ) * a(n-k).
MATHEMATICA
nmax = 45; A[_] = 0; Do[A[x_] = x - x^2 Exp[Sum[A[x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = 1; a[2] = -1; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 45}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 16 2023
STATUS
approved