login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A189731 A342140 A126354 * A158939 A173795 A249769
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 12 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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