OFFSET
0,4
COMMENTS
Half the number of block sizes are even and the other half are odd.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..576
Wikipedia, Partition of a set
FORMULA
EXAMPLE
a(0) = 1: () the empty partition.
a(1) = 0.
a(2) = 0.
a(3) = 3: 12|3, 13|2, 1|23.
a(4) = 0.
a(5) = 15: 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 12|345, 1345|2, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234, 1|2345.
a(6) = 45: 12|34|5|6, 12|35|4|6, 12|3|45|6, 12|36|4|5, 12|3|46|5, 12|3|4|56, 13|24|5|6, 13|25|4|6, 13|2|45|6, 13|26|4|5, 13|2|46|5, 13|2|4|56, 14|23|5|6, 15|23|4|6, 1|23|45|6, 16|23|4|5, 1|23|46|5, 1|23|4|56, 14|25|3|6, 14|2|35|6, 14|26|3|5, 14|2|36|5, 14|2|3|56, 15|24|3|6, 1|24|35|6, 16|24|3|5, 1|24|36|5, 1|24|3|56, 15|2|34|6, 1|25|34|6, 16|2|34|5, 1|26|34|5, 1|2|34|56, 15|26|3|4, 15|2|36|4, 15|2|3|46, 16|25|3|4, 1|25|36|4, 1|25|3|46, 16|2|35|4, 1|26|35|4, 1|2|35|46, 16|2|3|45, 1|26|3|45, 1|2|36|45.
MAPLE
b:= proc(n, x, y) option remember; `if`(abs(x-y)>2*n, 0,
`if`(n=0, 1, b(n-1, x+1, y)+`if`(x>0, b(n-1, x-1, y+1)*x, 0)+
`if`(y>0, b(n-1, x+1, y-1)*y, 0)))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..33);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 12 2023
STATUS
approved