%I #11 May 24 2018 12:07:04

%S 1,1,3,13,75,540,4670,47110,543130,7044450,101519250,1609319250,

%T 27830729850,521397676800,10519576867800,227400111939000,

%U 5243385642495000,128458209887007000,3332234177825553000,91241046790816923000,2629791992312269785000

%N Number of ordered set partitions of [n] with at most four elements per block.

%H Alois P. Heinz, <a href="/A276924/b276924.txt">Table of n, a(n) for n = 0..424</a>

%F E.g.f.: 1/(1-Sum_{i=1..4} x^i/i!).

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

%p a(n-i)*binomial(n, i), i=1..min(n, 4)))

%p end:

%p seq(a(n), n=0..25);

%p # second Maple program:

%p a:= n-> n!*(<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1/24|1/6|1/2|1>>^n)[4, 4]:

%p seq(a(n), n=0..25);

%t max = 20; CoefficientList[1/(1-Sum[x^i/i!, {i, 1, 4}]) + O[x]^(max+1), x]* Range[0, max]! (* _Jean-François Alcover_, May 24 2018 *)

%Y Column k=4 of A276921.

%Y Cf. A001681.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 22 2016