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

Author

Alois P. Heinz, Jun 10 2023

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..303
• Wikipedia, Partition of a set

Crossrefs

Bisection of A290383 (odd part).

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

Programs

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);

Formula

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