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A320758 Number of ordered set partitions of [n] where the maximal block size equals two.

%I A320758 #10 Dec 14 2020 05:13:10
%S A320758 1,6,42,330,2970,30240,345240,4377240,61122600,933055200,15470254800,
%T A320758 277005128400,5329454130000,109681187616000,2404894892400000,
%U A320758 55977698400624000,1378748676601296000,35829233832135744000,979763376201049440000,28124715476056399200000
%N A320758 Number of ordered set partitions of [n] where the maximal block size equals two.
%H A320758 Alois P. Heinz, <a href="/A320758/b320758.txt">Table of n, a(n) for n = 2..428</a>
%F A320758 E.g.f.: 1/(1-Sum_{i=1..2} x^i/i!) - 1/(1-x).
%F A320758 A(n) = A080599(n) - A000142(n).
%p A320758 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A320758       b(n-i, k)*binomial(n, i), i=1..min(n, k)))
%p A320758     end:
%p A320758 a:= n-> (k-> b(n, k) -b(n, k-1))(2):
%p A320758 seq(a(n), n=2..25);
%t A320758 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];
%t A320758 a[n_] := With[{k = 2}, b[n, k] - b[n, k-1]];
%t A320758 a /@ Range[2, 25] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)
%Y A320758 Column k=2 of A276922.
%Y A320758 Cf. A000142, A080599.
%K A320758 nonn
%O A320758 2,2
%A A320758 _Alois P. Heinz_, Oct 20 2018