OFFSET
1,5
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} (-1)^(k/d+1) * d * a(d) ) * a(n-k).
MATHEMATICA
nmax = 40; A[_] = 0; Do[A[x_] = x - x^2 Exp[Sum[(-1)^(k + 1) 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[(-1)^(k/d + 1) d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 40}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 18 2023
STATUS
approved