A363549 Total number of parity changes within all partitions of [n].

0, 0, 2, 9, 35, 152, 690, 3476, 18362, 105507, 633439, 4077386, 27317322, 194202164, 1431942154, 11117639073, 89255122863, 750051307896, 6500488706254, 58693723144324, 545325034579386, 5258317906940219, 52072378163037347, 533479904210984930, 5603461526474415150

Offset: 0

Author

Alois P. Heinz, Jun 09 2023

Keywords

• nonn

Comments

The blocks are ordered with increasing least elements.

Examples

			a(3) = 9 = 1*1 + 4*2: 13|2, 123, 12|3, 1|23, 1|2|3.
a(4) = 35 = 3*1 + 4*2 + 8*3: 134|2, 13|24, 13|2|4, 124|3, 14|23, 14|2|3, 1|24|3, 1234, 123|4, 12|34, 12|3|4, 1|234, 1|23|4, 1|2|34, 1|2|3|4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..28
• Wikipedia, Partition of a set

Crossrefs

Cf. A000110, A363496, A363519.

Formula

a(n) = Sum_{k=0..max(0,n-1)} k * A363519(n,k).