A363496 Total number of parity changes within the blocks of all partitions of [n].

0, 0, 1, 4, 17, 74, 356, 1808, 9923, 57442, 354407, 2296028, 15704028, 112266048, 841442105, 6564854864, 53413489773, 450789496454, 3950844987040, 35809477617544, 335901221506491, 3250110998386534, 32453151223493139, 333520967584364248, 3528754456836294712

Offset: 0

Author

Alois P. Heinz, Jun 05 2023

Keywords

• nonn

Examples

			a(4) = 17 = 6*1 + 4*2 + 1*3: 124|3, 12|3|4, 134|2, 1|23|4, 14|2|3, 1|2|34, 123|4, 12|34, 14|23, 1|234, 1234.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..575
• Wikipedia, Partition of a set

Crossrefs

Cf. A000110, A077613, A363493, A363549.

Programs

Maple

b:= proc(n, x, y) option remember; `if`(n=0, [1, 0],
     `if`(y=0, 0, (p-> p+[0, p[1]])(b(n-1, y-1, x+1)*y))+
        b(n-1, y, x)*x + b(n-1, y, x+1))
    end:
a:= n-> b(n, 0$2)[2]:
seq(a(n), n=0..24);

Formula

a(n) = Sum_{k=0..max(0,n-1)} k * A363493(n,k).