A305785 Number of set partitions of [n] with alternating parity of elements and exactly ceiling(n/2) blocks.
1, 1, 1, 2, 3, 7, 14, 33, 84, 204, 627, 1558, 5692, 14402, 60752, 155828, 747046, 1937292, 10385051, 27176489, 161160411, 424958631, 2760858706, 7327447983, 51762453941, 138150105263, 1054164297384, 2827224795106, 23174732414244, 62420125297576, 546984814641114
Offset: 0
Keywords
Examples
a(5) = 7: 123|4|5, 12|34|5, 12|3|45, 1|234|5, 145|2|3, 1|2|345, 1|23|45.
Links
- Wikipedia, Partition of a set
Crossrefs
Cf. A274581.
Formula
a(n) = A274581(n,ceiling(n/2)).