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 A362893 Number of partitions of [n] whose blocks can be ordered such that the i-th block has at least i elements and no block j > i has an element smaller than the i-th smallest element of block i. 3
 1, 1, 1, 2, 5, 12, 28, 69, 193, 614, 2103, 7359, 25660, 88914, 309502, 1102146, 4092840, 16046224, 66410789, 286905421, 1273646720, 5729762139, 25881820352, 116872997038, 527375160184, 2384407416357, 10856086444051, 50097994816979, 235937202788389 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..890 Wikipedia, Partition of a set EXAMPLE a(0) = 1: (), the empty partition. a(1) = 1: 1. a(2) = 1: 12. a(3) = 2: 123, 1|23. a(4) = 5: 1234, 12|34, 13|24, 14|23, 1|234. a(5) = 12: 12345, 123|45, 124|35, 125|34, 12|345, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234, 1|2345. a(6) = 28: 123456, 1234|56, 1235|46, 1236|45, 123|456, 1245|36, 1246|35, 124|356, 1256|34, 125|346, 126|345, 12|3456, 1345|26, 1346|25, 134|256, 1356|24, 135|246, 136|245, 13|2456, 1456|23, 145|236, 146|235, 14|2356, 156|234, 15|2346, 16|2345, 1|23456, 1|23|456. a(7) = 69: 1234567, 12345|67, 12346|57, 12347|56, 1234|567, 12356|47, 12357|46, 1235|467, 12367|45, 1236|457, 1237|456, 123|4567, 12456|37, 12457|36, 1245|367, 12467|35, 1246|357, 1247|356, 124|3567, 12567|34, 1256|347, 1257|346, 125|3467, 1267|345, 126|3457, 127|3456, 12|34567, 12|34|567, 13456|27, 13457|26, 1345|267, 13467|25, 1346|257, 1347|256, 134|2567, 13567|24, 1356|247, 1357|246, 135|2467, 1367|245, 136|2457, 137|2456, 13|24567, 13|24|567, 14567|23, 1456|237, 1457|236, 145|2367, 1467|235, 146|2357, 147|2356, 14|23567, 14|23|567, 1567|234, 156|2347, 157|2346, 15|23467, 167|2345, 16|23457, 17|23456, 1|234567, 1|234|567, 15|23|467, 1|235|467, 16|23|457, 1|236|457, 17|23|456, 1|237|456, 1|23|4567. MAPLE b:= proc(n, t) option remember; `if`(n=0 or n=t, 1, add(b(n-j, t+1)*binomial(n-t, j-t), j=t..n)) end: a:= n-> b(n, 1): seq(a(n), n=0..28); CROSSREFS Cf. A000110, A362549, A362635. Sequence in context: A024960 A291234 A346051 * A326760 A238828 A326761 Adjacent sequences: A362890 A362891 A362892 * A362894 A362895 A362896 KEYWORD nonn AUTHOR Alois P. Heinz, May 08 2023 STATUS approved

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Last modified February 23 11:05 EST 2024. Contains 370283 sequences. (Running on oeis4.)