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A276924 Number of ordered set partitions of [n] with at most four elements per block.

%I A276924 #11 May 24 2018 12:07:04
%S A276924 1,1,3,13,75,540,4670,47110,543130,7044450,101519250,1609319250,
%T A276924 27830729850,521397676800,10519576867800,227400111939000,
%U A276924 5243385642495000,128458209887007000,3332234177825553000,91241046790816923000,2629791992312269785000
%N A276924 Number of ordered set partitions of [n] with at most four elements per block.
%H A276924 Alois P. Heinz, <a href="/A276924/b276924.txt">Table of n, a(n) for n = 0..424</a>
%F A276924 E.g.f.: 1/(1-Sum_{i=1..4} x^i/i!).
%p A276924 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A276924        a(n-i)*binomial(n, i), i=1..min(n, 4)))
%p A276924     end:
%p A276924 seq(a(n), n=0..25);
%p A276924 # second Maple program:
%p A276924 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 A276924 seq(a(n), n=0..25);
%t A276924 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 A276924 Column k=4 of A276921.
%Y A276924 Cf. A001681.
%K A276924 nonn
%O A276924 0,3
%A A276924 _Alois P. Heinz_, Sep 22 2016