OFFSET
0,3
COMMENTS
Euler transform of A163767.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^A163767(k).
MAPLE
A:= proc(n, k) option remember; `if`(k=1, 1,
add(A(d, k-1), d=numtheory[divisors](n)))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
A(d$2), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..40); # Alois P. Heinz, May 22 2018
MATHEMATICA
nmax = 34; CoefficientList[Series[Product[1/(1 - x^k)^Times@@(Binomial[# + k - 1, k - 1]&/@FactorInteger[k][[All, 2]]), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d Times@@(Binomial[# + d - 1, d - 1]&/@FactorInteger[d][[All, 2]]), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 34}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 22 2018
STATUS
approved