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

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Wikipedia, Partition of a set

Example

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

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);

Crossrefs

Column k=2 of A363493.

Cf. A000110.

Sequence in context: A268431 A033114 A096881 * A344217 A033122 A330246

Adjacent sequences: A363585 A363586 A363587 * A363589 A363590 A363591

Keyword

nonn

Author

Alois P. Heinz, Jun 10 2023

Status

approved