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

%I A367450 #24 Dec 21 2023 21:52:47
%S A367450 1,0,1,0,1,4,12,55,198,979,4700,22288,131612,754614,4833776,32539094,
%T A367450 225628769,1675660796,12676652631,100996809180,830086817650,
%U A367450 7065404491242
%N A367450 Number of partitions of [n] whose sum of block maxima equals twice the sum of block minima.
%H A367450 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A367450 a(0) = 1: the empty partition.
%e A367450 a(2) = 1: 12.
%e A367450 a(4) = 1: 134|2.
%e A367450 a(5) = 4: 1245|3, 1|2345, 14|25|3, 15|24|3.
%e A367450 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.
%p A367450 b:= proc(n, m, s) option remember;
%p A367450      `if`(n=0, `if`(add(i, i=m)*2=s, 1, 0),
%p A367450       add(b(n-1, subs(j=n, m), s), j=m)+
%p A367450           b(n-1, {m[], n}, s+n))
%p A367450     end:
%p A367450 a:= n-> b(n, {}, 0):
%p A367450 seq(a(n), n=0..15);
%Y A367450 Cf. A000110, A368338.
%K A367450 nonn,more
%O A367450 0,6
%A A367450 _Alois P. Heinz_, Dec 15 2023