OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1650
FORMULA
a(n) = 1/n * [x^n] Product_{j=1..n} (1+(n-1)*x^j)/(1-x^j) for n>0, a(0)=1.
a(n) = A321880(n)/n for n > 0, a(0) = 1.
EXAMPLE
a(3) = 5: 3a, 2a1a, 2a1b, 2a1c, 111a.
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, k*add(
(t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i) +b(n, i-1, k)))
end:
a:= n-> `if`(n=0, 1, b(n$3)/n):
seq(a(n), n=0..34);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, k Sum[With[{t = n - i j}, b[t, Min[t, i - 1], k]], {j, 1, n/i}] + b[n, i - 1, k]]];
a[n_] := If[n == 0, 1, b[n, n, n]/n];
a /@ Range[0, 34] (* Jean-François Alcover, Dec 15 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 08 2019
STATUS
approved