OFFSET
0,5
COMMENTS
Logarithmic transform of A000009.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..470
N. J. A. Sloane, Transforms
FORMULA
E.g.f.: log(Sum_{k>=0} A000009(k)*x^k/k!).
EXAMPLE
E.g.f.: A(x) = x/1! + x^3/3! - 3*x^4/4! + 7*x^5/5! - 24*x^6/6! + 130*x^7/7! - 748*x^8/8! + ...
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
`if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
end:
a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n)-add(
j*a(j)*binomial(n, j)*t(n-j), j=1..n-1)/n))(b)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Mar 07 2018
MATHEMATICA
nmax = 24; CoefficientList[Series[Log[Sum[PartitionsQ[k] x^k/k!, {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = PartitionsQ[n] - Sum[k Binomial[n, k] PartitionsQ[n - k] a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 24}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Mar 07 2018
STATUS
approved