A367450 Number of partitions of [n] whose sum of block maxima equals twice the sum of block minima.

1, 0, 1, 0, 1, 4, 12, 55, 198, 979, 4700, 22288, 131612, 754614, 4833776, 32539094, 225628769, 1675660796, 12676652631, 100996809180, 830086817650, 7065404491242

Offset: 0

Author

Alois P. Heinz, Dec 15 2023

Keywords

• nonn
• more

Examples

			a(0) = 1: the empty partition.
a(2) = 1: 12.
a(4) = 1: 134|2.
a(5) = 4: 1245|3, 1|2345, 14|25|3, 15|24|3.
a(6) = 12: 12356|4, 12|3456, 13|25|46, 13|26|45, 15|23|46, 16|23|45, 14|2|356, 1|245|36, 1|246|35, 156|2|34, 1|25|346, 1|26|345.
		

Links

• Wikipedia, Partition of a set

Crossrefs

Cf. A000110, A368338.

Programs

Maple

b:= proc(n, m, s) option remember;
     `if`(n=0, `if`(add(i, i=m)*2=s, 1, 0),
      add(b(n-1, subs(j=n, m), s), j=m)+
          b(n-1, {m[], n}, s+n))
    end:
a:= n-> b(n, {}, 0):
seq(a(n), n=0..15);