OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
FORMULA
a(n) = Sum_{k=1..n} k * A327116(n,k).
MAPLE
C:= binomial:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
b(n-i*j, min(n-i*j, i-1), k)*C(C(k+i-1, i), j), j=0..n/i)))
end:
a:= n-> add(k*add(b(n$2, i)*(-1)^(k-i)*C(k, i), i=0..k), k=0..n):
seq(a(n), n=0..23);
MATHEMATICA
c = Binomial;
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, Min[n - i*j, i - 1], k] c[c[k + i - 1, i], j], {j, 0, n/i}]]];
a[n_] := Sum[k Sum[b[n, n, i] (-1)^(k - i) c[k, i], {i, 0, k}], {k, 0, n}];
a /@ Range[0, 23] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2019
STATUS
approved