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 A362639 Number of partitions of [n] whose blocks are ordered with increasing least elements and where block i (except possibly the last) has size i. 2
 1, 1, 1, 1, 2, 3, 4, 15, 36, 70, 120, 756, 2800, 7920, 18900, 40040, 388080, 2106000, 8408400, 27489000, 77837760, 197520960, 2756754000, 20903929200, 113809696000, 497097881280, 1847907341280, 6062876820000, 17990209036800, 343877493960000, 3501594297801600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..724 Wikipedia, Partition of a set EXAMPLE a(0) = 1: (), the empty partition. a(1) = 1: 1. a(2) = 1: 1|2. a(3) = 1: 1|23. a(4) = 2: 1|23|4, 1|24|3. a(5) = 3: 1|23|45, 1|24|35, 1|25|34. a(6) = 4: 1|23|456, 1|24|356, 1|25|346, 1|26|345. a(7) = 15: 1|23|456|7, 1|23|457|6, 1|23|467|5, 1|24|356|7, 1|24|357|6, 1|24|367|5, 1|25|346|7, 1|25|347|6, 1|26|345|7, 1|27|345|6, 1|26|347|5, 1|27|346|5, 1|25|367|4, 1|26|357|4, 1|27|356|4. MAPLE b:= proc(n, t) option remember; `if`(n<=t, 1, b(n-t, t+1)*binomial(n-1, t-1)) end: a:= n-> b(n, 1): seq(a(n), n=0..30); CROSSREFS Cf. A000110, A362637. Sequence in context: A103096 A295757 A005645 * A348628 A281586 A365739 Adjacent sequences: A362636 A362637 A362638 * A362640 A362641 A362642 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 28 2023 STATUS approved

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Last modified August 9 10:37 EDT 2024. Contains 375040 sequences. (Running on oeis4.)