OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..139
Wikipedia, Partition of a set
FORMULA
a(n) = A323128(2n,n).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, add(k!/(k-j)!
*binomial(n-1, j-1)*b(n-j, k), j=1..min(k, n)))
end:
a:= n-> add(b(2*n, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..15);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[k!/(k-j)! Binomial[n - 1, j - 1]* b[n - j, k], {j, 1, Min[k, n]}]];
a[n_] := Sum[b[2n, n - i] (-1)^i Binomial[n, i], {i, 0, n}];
a /@ Range[0, 15] (* Jean-François Alcover, May 05 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2019
STATUS
approved