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A320759 Number of ordered set partitions of [n] where the maximal block size equals three.

%I A320759 #7 Dec 14 2020 05:13:21
%S A320759 1,8,80,860,10290,136080,1977360,31365600,539847000,10026139200,
%T A320759 199937337600,4262167509600,96744738090000,2329950823200000,
%U A320759 59348032327584000,1594257675506496000,45047749044458160000,1335740755933584000000,41473196779273459200000
%N A320759 Number of ordered set partitions of [n] where the maximal block size equals three.
%H A320759 Alois P. Heinz, <a href="/A320759/b320759.txt">Table of n, a(n) for n = 3..424</a>
%F A320759 E.g.f.: 1/(1-Sum_{i=1..3} x^i/i!) - 1/(1-Sum_{i=1..2} x^i/i!).
%F A320759 a(n) = A189886(n) - A080599(n).
%p A320759 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A320759       b(n-i, k)*binomial(n, i), i=1..min(n, k)))
%p A320759     end:
%p A320759 a:= n-> (k-> b(n, k) -b(n, k-1))(3):
%p A320759 seq(a(n), n=3..25);
%t A320759 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];
%t A320759 a[n_] := With[{k = 3}, b[n, k] - b[n, k-1]];
%t A320759 a /@ Range[3, 25] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)
%Y A320759 Column k=3 of A276922.
%Y A320759 Cf. A080599, A189886.
%K A320759 nonn
%O A320759 3,2
%A A320759 _Alois P. Heinz_, Oct 20 2018