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URL: https://oeis.org/A363429

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A363429
Number of set partitions of [n] such that each block has at most one even element.
2
1, 1, 2, 5, 10, 37, 77, 372, 799, 4736, 10427, 73013, 163967, 1322035, 3017562, 27499083, 63625324, 646147067, 1512354975, 16926317722, 40012800675, 489109544320, 1166271373797, 15455199988077, 37134022033885, 530149003318273, 1282405154139046, 19619325078384593
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..ceiling(n/2)} floor(n/2)^k * binomial(ceiling(n/2),k) * Bell(ceiling(n/2)-k).
EXAMPLE
a(0) = 1: () the empty partition.
a(1) = 1: 1.
a(2) = 2: 12, 1|2.
a(3) = 5: 123, 12|3, 13|2, 1|23, 1|2|3.
a(4) = 10: 123|4, 12|34, 12|3|4, 134|2, 13|2|4, 14|23, 1|23|4, 14|2|3, 1|2|34, 1|2|3|4.
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(n-h, h))(iquo(n, 2)):
seq(a(n), n=0..30);
CROSSREFS
Bisection gives: A134980 (even part).
Cf. A000110, A110132 (exactly one even), A124421 (at least one even), A363430 (at most one odd).
Sequence in context: A144636 A320430 A018418 * A290032 A155217 A004143
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 01 2023
STATUS
approved