OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..110
Wikipedia, Partition of a set
FORMULA
a(n) = A363493(2n+1,n).
EXAMPLE
a(0) = 1: 1.
a(1) = 2: 12|3, 1|23.
a(2) = 17: 1235|4, 123|4|5, 1245|3, 12|34|5, 125|3|4, 12|3|45, 1345|2, 134|25, 14|235, 14|23|5, 15|234, 1|234|5, 1|23|45, 145|2|3, 14|25|3, 1|25|34, 1|2|345.
MAPLE
b:= proc(n, x, y) option remember; `if`(n=0, 1,
`if`(y=0, 0, expand(b(n-1, y-1, x+1)*y*z))+
b(n-1, y, x)*x + b(n-1, y, x+1))
end:
a:= n-> coeff(b(2*n+1, 0$2), z, n):
seq(a(n), n=0..17);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2023
STATUS
approved