OFFSET
0,3
COMMENTS
a(n)/n! is the Euler transform of [1, 1 + 1/2, 1 + 1/2 + 1/3, 1 + 1/2 + 1/3 + 1/4, ...].
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..436
N. J. A. Sloane, Transforms
MAPLE
H:= proc(n) option remember; `if`(n=0, 0, 1/n+H(n-1)) end:
b:= proc(n) option remember; `if`(n=0, 1, add(add(d*
H(d), d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
end:
a:= n-> n!*b(n):
seq(a(n), n=0..20); # Alois P. Heinz, May 03 2018
MATHEMATICA
nmax = 22; CoefficientList[Series[Product[1/(1 - x^k)^HarmonicNumber[k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d HarmonicNumber[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 03 2018
STATUS
approved