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%I #9 May 07 2016 09:02:38
%S 1,3,18,90,630,4410,37800,340200,3515400,38669400,471517200,
%T 6129723600,86497210800,1297458162000,20841060240000,354298024080000,
%U 6389869069584000,121407512322096000,2430526127309280000,51041048673494880000,1123451899297247520000
%N Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to two.
%H Alois P. Heinz, <a href="/A272492/b272492.txt">Table of n, a(n) for n = 2..450</a>
%F E.g.f.: x^2 * Product_{i=1..2} (i-1)!/(i!-x^i).
%F 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
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p end:
%p a:= n-> (k-> b(n, k) -b(n, k-1))(2):
%p seq(a(n), n=2..30);
%t Table[n!*(1 + ((-1)^n*(Sqrt[2] - 1) - Sqrt[2] - 1)/2^(n/2 + 1)), {n, 2, 20}] (* _Vaclav Kotesovec_, May 07 2016 *)
%Y Column k=2 of A262071.
%K nonn
%O 2,2
%A _Alois P. Heinz_, May 01 2016
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