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Total number of parity changes within all partitions of [n].
3

%I #17 Jun 12 2023 17:25:11

%S 0,0,2,9,35,152,690,3476,18362,105507,633439,4077386,27317322,

%T 194202164,1431942154,11117639073,89255122863,750051307896,

%U 6500488706254,58693723144324,545325034579386,5258317906940219,52072378163037347,533479904210984930,5603461526474415150

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

%C The blocks are ordered with increasing least elements.

%H Alois P. Heinz, <a href="/A363549/b363549.txt">Table of n, a(n) for n = 0..28</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

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

%e a(3) = 9 = 1*1 + 4*2: 13|2, 123, 12|3, 1|23, 1|2|3.

%e 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.

%Y Cf. A000110, A363496, A363519.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 09 2023