OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..175
Wikipedia, Partition (number theory)
FORMULA
a(n) = A326500(2n,n).
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add((t->
b(n-t, min(n-t, i-1), k)*binomial(k+t-1, t))(i*j), j=0..n/i)))
end:
a:= n-> add(b(2*n$2, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..18);
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[k + i j - 1, i j], {j, 0, n/i}]]];
a[n_] := Sum[b[2n, 2n, n-i] (-1)^i Binomial[n, i], {i, 0, n}];
a /@ Range[0, 18] (* Jean-François Alcover, May 08 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2019
STATUS
approved