A363589 Number of partitions of [2n+1] such that the largest element of each block is odd.

1, 2, 8, 56, 584, 8360, 155720, 3633704, 103284296, 3499082408, 138860069192, 6364334129192, 332934707138888, 19681714722718376, 1303617735072968264, 96028608749005335080, 7816178772774327523400, 698943538498179895072424, 68316963055524325115842376

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..303

Wikipedia, Partition of a set

Formula

a(n) = A290383(2*n+1).

Example

a(0) = 1: 1.
a(1) = 2: 123, 1|23.
a(2) = 8: 12345, 123|45, 1245|3, 13|245, 145|23, 1|2345, 1|23|45, 1|245|3.

Maple

b:= proc(n, x, y) option remember; `if`(n=0, 1, `if`(n::even, 0,
      b(n-1, y, x+1))+b(n-1, y, x)*x+b(n-1, y, x)*y)
    end:
a:= n-> b(2*n+1, 0$2):
seq(a(n), n=0..20);

Crossrefs

Bisection of A290383 (odd part).

Cf. A000110, A307375 (the largest element of each block is even).

Sequence in context: A349562 A325290 A197949 * A243953 A005439 A128814

Adjacent sequences: A363586 A363587 A363588 * A363590 A363591 A363592

Keyword

nonn

Author

Alois P. Heinz, Jun 10 2023

Status

approved