OFFSET
0,4
COMMENTS
Invert transform of A008683.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..5000
N. J. A. Sloane, Transforms
FORMULA
G.f.: 1/(1 - Sum_{k>=1} A008683(k)*x^k).
a(0) = 1; a(n) = Sum_{k=1..n} mu(k) * a(n-k). - Seiichi Manyama, Apr 06 2022
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
numtheory[mobius](j)*a(n-j), j=1..n))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Mar 10 2018
MATHEMATICA
nmax = 47; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[MoebiusMu[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 47}]
PROG
(PARI) my(N=66, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, moebius(k)*x^k))) \\ Seiichi Manyama, Apr 06 2022
(PARI) a(n) = if(n==0, 1, sum(k=1, n, moebius(k)*a(n-k))); \\ Seiichi Manyama, Apr 06 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Mar 10 2018
STATUS
approved