OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..230
Wikipedia, Partition (number theory)
FORMULA
a(n) = Sum_{k=1..n} k * A327117(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)+j-1, 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..25);
MATHEMATICA
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] Binomial[Binomial[k, i]+j-1, j], {j, 0, n/i}]]];
a[n_] := Sum[k Sum[b[n, n, i](-1)^(k-i)Binomial[k, i], {i, 0, k}], {k, 0, n}];
a /@ Range[0, 25] (* Jean-François Alcover, May 06 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 13 2019
STATUS
approved