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A356907
Expansion of 1 / (1 + Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).
0
1, -1, 2, -2, 2, 0, -4, 12, -22, 34, -42, 38, -6, -68, 202, -394, 616, -782, 730, -204, -1104, 3486, -6994, 11142, -14452, 14026, -5296, -17558, 60042, -123860, 201128, -266384, 268176, -124034, -273626, 1030396, -2188864, 3624290, -4898740, 5101306, -2744408
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = -Sum_{k=1..n} A008836(k) * a(n-k).
MATHEMATICA
nmax = 40; CoefficientList[Series[1/(1 + Sum[LiouvilleLambda[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[LiouvilleLambda[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 40}]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Oct 02 2022
STATUS
approved