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A363495
Number of partitions of [2n+1] having exactly n parity changes within their blocks.
2
1, 2, 17, 202, 3899, 98282, 3270604, 134513166, 6744026175, 400657370384, 27819913699591, 2222485356153758, 202085549223540498, 20700107045049813072, 2369116259054858660518, 300712325745715659503258, 42064844140178917094949029, 6448050588990736076081469470
OFFSET
0,2
LINKS
FORMULA
a(n) = A363493(2n+1,n).
EXAMPLE
a(0) = 1: 1.
a(1) = 2: 12|3, 1|23.
a(2) = 17: 1235|4, 123|4|5, 1245|3, 12|34|5, 125|3|4, 12|3|45, 1345|2, 134|25, 14|235, 14|23|5, 15|234, 1|234|5, 1|23|45, 145|2|3, 14|25|3, 1|25|34, 1|2|345.
MAPLE
b:= proc(n, x, y) option remember; `if`(n=0, 1,
`if`(y=0, 0, expand(b(n-1, y-1, x+1)*y*z))+
b(n-1, y, x)*x + b(n-1, y, x+1))
end:
a:= n-> coeff(b(2*n+1, 0$2), z, n):
seq(a(n), n=0..17);
CROSSREFS
Cf. A363493.
Sequence in context: A367839 A126752 A234461 * A277768 A364335 A364446
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 05 2023
STATUS
approved