A363495 Number of partitions of [2n+1] having exactly n parity changes within their blocks.

1, 2, 17, 202, 3899, 98282, 3270604, 134513166, 6744026175, 400657370384, 27819913699591, 2222485356153758, 202085549223540498, 20700107045049813072, 2369116259054858660518, 300712325745715659503258, 42064844140178917094949029, 6448050588990736076081469470

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..110

Wikipedia, Partition of a set

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: A126752 A378690 A234461 * A277768 A364335 A364446

Adjacent sequences: A363492 A363493 A363494 * A363496 A363497 A363498

Keyword

nonn

Author

Alois P. Heinz, Jun 05 2023

Status

approved