A363430 Number of set partitions of [n] such that each block has at most one odd element.
1, 1, 2, 3, 10, 17, 77, 141, 799, 1540, 10427, 20878, 163967, 338233, 3017562, 6376149, 63625324, 137144475, 1512354975, 3315122947, 40012800675, 88981537570, 1166271373797, 2626214876310, 37134022033885, 84540738911653, 1282405154139046, 2948058074576995
Offset: 0
Keywords
Examples
a(0) = 1: () the empty partition. a(1) = 1: 1. a(2) = 2: 12, 1|2. a(3) = 3: 12|3, 1|23, 1|2|3. a(4) = 10: 124|3, 12|34, 12|3|4, 14|23, 1|234, 1|23|4, 14|2|3, 1|24|3, 1|2|34, 1|2|3|4. a(5) = 17: 124|3|5, 12|34|5, 12|3|45, 12|3|4|5, 14|23|5, 1|234|5, 1|23|45, 1|23|4|5, 14|25|3, 14|2|3|5, 1|245|3, 1|24|3|5, 1|25|34, 1|2|34|5, 1|25|3|4, 1|2|3|45, 1|2|3|4|5.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..773
- Wikipedia, Partition of a set
Crossrefs
Programs
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Maple
b:= proc(n, m) option remember; `if`(n=0, 1, b(n-1, m+1)+m*b(n-1, m)) end: a:= n-> (h-> b(h, n-h))(iquo(n, 2)): seq(a(n), n=0..30);
Formula
a(n) = Sum_{k=0..floor(n/2)} ceiling(n/2)^k * binomial(floor(n/2),k) * Bell(floor(n/2)-k).