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A362638
Number of partitions of [n] whose blocks are ordered with increasing least elements and where block i has size at most i.
2
1, 1, 1, 2, 4, 11, 34, 117, 458, 1960, 9113, 45730, 246220, 1411820, 8584314, 55121249, 372445462, 2639750490, 19570232608, 151390999949, 1219308754065, 10204045406690, 88571532840007, 796100505025761, 7398510884959638, 70995106473861076, 702542384597885615
OFFSET
0,4
LINKS
EXAMPLE
a(0) = 1: ().
a(1) = 1: 1.
a(2) = 1: 1|2.
a(3) = 2: 1|23, 1|2|3.
a(4) = 4: 1|23|4, 1|24|3, 1|2|34, 1|2|3|4.
a(5) = 11: 1|23|45, 1|23|4|5, 1|24|35, 1|24|3|5, 1|25|34, 1|2|345, 1|2|34|5, 1|25|3|4, 1|2|35|4, 1|2|3|45, 1|2|3|4|5.
a(6) = 34: 1|23|456, 1|23|45|6, 1|23|46|5, 1|23|4|56, 1|23|4|5|6, 1|24|356, 1|24|35|6, 1|24|36|5, 1|24|3|56, 1|24|3|5|6, 1|25|346, 1|25|34|6, 1|26|345, 1|2|345|6, 1|26|34|5, 1|2|346|5, 1|2|34|56, 1|2|34|5|6, 1|25|36|4, 1|25|3|46, 1|25|3|4|6, 1|26|35|4, 1|2|356|4, 1|2|35|46, 1|2|35|4|6, 1|26|3|45, 1|2|36|45, 1|2|3|456, 1|2|3|45|6, 1|26|3|4|5, 1|2|36|4|5, 1|2|3|46|5, 1|2|3|4|56, 1|2|3|4|5|6.
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1, add(
b(n-j, t+1)*binomial(n-1, j-1), j=1..min(t, n)))
end:
a:= n-> b(n, 1):
seq(a(n), n=0..30);
CROSSREFS
Sequence in context: A099215 A089407 A289588 * A344489 A238425 A358075
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 28 2023
STATUS
approved