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 A361084 Number of partitions of [n] such that in each block the smallest element and the largest element have opposite parities. 2
 1, 0, 1, 0, 3, 2, 17, 28, 171, 430, 2617, 8496, 54739, 214714, 1477153, 6743204, 49550011, 256645926, 2010328585, 11602635128, 96590823907, 612918061426, 5404902119025, 37319203169580, 347468152001739, 2589081441826334, 25375080898848729, 202668739104752960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..165 Wikipedia, Partition of a set FORMULA a(n) mod 2 = A059841(n). EXAMPLE a(0) = 1: () the empty partition. a(1) = 0. a(2) = 1: 12. a(3) = 0. a(4) = 3: 1234, 12|34, 14|23. a(5) = 2: 134|25, 14|235. a(6) = 17: 123456, 1234|56, 1236|45, 124|356, 1256|34, 12|3456, 12|34|56, 12|36|45, 1346|25, 136|245, 1456|23, 146|235, 14|23|56, 16|2345, 16|23|45, 14|25|36, 16|25|34. a(7) = 28: 12356|47, 1236|457, 12|356|47, 12|36|457, 13456|27, 1346|257, 134|2567, 134|25|67, 134|27|56, 1356|247, 136|2457, 136|25|47, 136|27|45, 1456|237, 146|2357, 14|23567, 14|235|67, 14|237|56, 156|2347, 16|23457, 156|23|47, 16|235|47, 16|237|45, 16|23|457, 14|257|36, 14|27|356, 156|27|34, 16|257|34. MAPLE b:= proc(n, x, y, u, v) option remember; `if`(x+v>n, 0, `if`(n=0, 1, `if`(y=0, 0, b(n-1, v, u, y-1, x+1)*y)+b(n-1, v, u, y, x+1)+ `if`(v=0, 0, b(n-1, v-1, u+1, y, x)*v)+b(n-1, v, u, y, x)*(u+x))) end: a:= n-> b(n, 0\$4): seq(a(n), n=0..30); CROSSREFS Cf. A000110, A059841, A363592. Sequence in context: A189731 A342140 A126354 * A158939 A173795 A249769 Adjacent sequences: A361081 A361082 A361083 * A361085 A361086 A361087 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 12 2023 STATUS approved

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Last modified June 21 21:50 EDT 2024. Contains 373559 sequences. (Running on oeis4.)