OFFSET
0,3
COMMENTS
a(n) is the number of partitions of an 2n-set that contain at most n nonempty subsets.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..288
FORMULA
a(n) = A102661(2n,n) for n >= 1. - Alois P. Heinz, Jun 13 2023
MAPLE
b:= proc(n) option remember; `if`(n=0, 1,
add(expand(b(n-j)*binomial(n-1, j-1)*x), j=1..n))
end:
a:= n-> (p-> add(coeff(p, x, i), i=0..n))(b(2*n, 0)):
seq(a(n), n=0..17); # Alois P. Heinz, Jun 13 2023
PROG
(PARI) a(n) = sum(j=0, n, stirling(2*n, j, 2)); \\ Michel Marcus, Dec 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 27 2022
STATUS
approved