%I #7 Dec 14 2020 05:13:21

%S 1,8,80,860,10290,136080,1977360,31365600,539847000,10026139200,

%T 199937337600,4262167509600,96744738090000,2329950823200000,

%U 59348032327584000,1594257675506496000,45047749044458160000,1335740755933584000000,41473196779273459200000

%N Number of ordered set partitions of [n] where the maximal block size equals three.

%H Alois P. Heinz, <a href="/A320759/b320759.txt">Table of n, a(n) for n = 3..424</a>

%F E.g.f.: 1/(1-Sum_{i=1..3} x^i/i!) - 1/(1-Sum_{i=1..2} x^i/i!).

%F a(n) = A189886(n) - A080599(n).

%p b:= proc(n, k) option remember; `if`(n=0, 1, add(

%p b(n-i, k)*binomial(n, i), i=1..min(n, k)))

%p end:

%p a:= n-> (k-> b(n, k) -b(n, k-1))(3):

%p seq(a(n), n=3..25);

%t b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];

%t a[n_] := With[{k = 3}, b[n, k] - b[n, k-1]];

%t a /@ Range[3, 25] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)

%Y Column k=3 of A276922.

%Y Cf. A080599, A189886.

%K nonn

%O 3,2

%A _Alois P. Heinz_, Oct 20 2018