OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
FORMULA
a(n) = Sum_{k=0..n} k * A255903(n,k).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)*add(d*
binomial(d+k-1, k-1), d=numtheory[divisors](j)), j=1..n)/n)
end:
a:= n-> add(add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k)*k, k=0..n):
seq(a(n), n=0..25);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - j, k]*Sum[d*Binomial[d + k - 1, k - 1], {d, Divisors[j]}], {j, 1, n}]/n];
a[n_] := Sum[Sum[b[n, k-i]*(-1)^i*Binomial[k, i], {i, 0, k}]*k, {k, 0, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 08 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 23 2018
STATUS
approved