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A272492 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to two. 2
1, 3, 18, 90, 630, 4410, 37800, 340200, 3515400, 38669400, 471517200, 6129723600, 86497210800, 1297458162000, 20841060240000, 354298024080000, 6389869069584000, 121407512322096000, 2430526127309280000, 51041048673494880000, 1123451899297247520000 (list; graph; refs; listen; history; text; internal format)
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 A058409

Adjacent sequences:  A272489 A272490 A272491 * A272493 A272494 A272495

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified February 23 05:58 EST 2019. Contains 320411 sequences. (Running on oeis4.)