A272492 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to two.

1, 3, 18, 90, 630, 4410, 37800, 340200, 3515400, 38669400, 471517200, 6129723600, 86497210800, 1297458162000, 20841060240000, 354298024080000, 6389869069584000, 121407512322096000, 2430526127309280000, 51041048673494880000, 1123451899297247520000

Offset

2,2

Links

Alois P. Heinz, Table of n, a(n) for n = 2..450

Formula

E.g.f.: x^2 * Product_{i=1..2} (i-1)!/(i!-x^i).

Recurrence: 2*a(n) = 2*n*a(n-1) + (n-1)*n*a(n-2) - (n-2)*(n-1)*n*a(n-3). - Vaclav Kotesovec, May 07 2016

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
    end:
a:= n-> (k-> b(n, k) -b(n, k-1))(2):
seq(a(n), n=2..30);

Mathematica

Table[n!*(1 + ((-1)^n*(Sqrt[2] - 1) - Sqrt[2] - 1)/2^(n/2 + 1)), {n, 2, 20}] (* Vaclav Kotesovec, May 07 2016 *)

Crossrefs

Column k=2 of A262071.

Sequence in context: A147518 A088336 A133594 * A092691 A064671 A363647

Adjacent sequences: A272489 A272490 A272491 * A272493 A272494 A272495

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved