OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..441
FORMULA
MAPLE
H:= proc(n) H(n):= 1/n +`if`(n=1, 0, H(n-1)) end:
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, 1, b(n, i-1)+H(i)*b(n-i, min(n-i, i-1))))
end:
a:= n-> b(n$2)*n!:
seq(a(n), n=0..25); # Alois P. Heinz, May 27 2018
MATHEMATICA
nmax = 21; CoefficientList[Series[Product[(1 + HarmonicNumber[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[Exp[Sum[Sum[(-1)^(k + 1) HarmonicNumber[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d HarmonicNumber[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 27 2018
STATUS
approved