A363588 Number of partitions of [n] having exactly two parity changes within their blocks.

0, 0, 0, 1, 4, 17, 68, 292, 1252, 5670, 26114, 126073, 621914, 3206277, 16888898, 92771126, 519907322, 3032369590, 18012896770, 111155162265, 697399200274, 4537750415991, 29972920817228, 204993708306706, 1421278374189924, 10188372221843166, 73948157842293620

Offset: 0

Author

Alois P. Heinz, Jun 10 2023

Keywords

• nonn

Examples

			a(4) = 4: 123|4, 12|34, 14|23, 1|234.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• Wikipedia, Partition of a set

Crossrefs

Column k=2 of A363493.

Cf. A000110.

Programs

Maple

b:= proc(n, x, y) option remember; convert(series(
     `if`(n=0, 1, `if`(y=0, 0, expand(b(n-1, y-1, x+1)*y*z))
       +b(n-1, y, x)*x + b(n-1, y, x+1)), z, 3), polynom)
    end:
a:= n-> coeff(b(n, 0$2), z, 2):
seq(a(n), n=0..27);