cp's OEIS Frontend

A245854 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 1.

%I A245854 #8 Jul 29 2024 13:08:21
%S A245854 1,2,12,68,520,4542,46550,540136,7045020,101865410,1619046418,
%T A245854 28053492348,526430246264,10636085523910,230214619661790,
%U A245854 5314695463338704,130356558777712468,3385311352838750538,92797887464933030762,2677623216872061223780,81123642038690958720048
%N A245854 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 1.
%H A245854 Alois P. Heinz, <a href="/A245854/b245854.txt">Table of n, a(n) for n = 1..400</a>
%F A245854 E.g.f.: 1/(2-exp(x))-1/(2-exp(x)+x).
%F A245854 a(n) = A000670(n) - A032032(n) = A245732(n,1) - A245732(n,2).
%p A245854 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A245854       add(b(n-j, k)*binomial(n, j), j=k..n))
%p A245854     end:
%p A245854 a:= n-> b(n, 1) -b(n, 2):
%p A245854 seq(a(n), n=1..25);
%t A245854 With[{nn=30},CoefficientList[Series[1/(2-Exp[x])-1/(2-Exp[x]+x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 29 2024 *)
%Y A245854 Column k=1 of A245733.
%Y A245854 Cf. A000670, A032032, A245732.
%K A245854 nonn
%O A245854 1,2
%A A245854 _Alois P. Heinz_, Aug 04 2014