A245854 - OEIS

%I #8 Jul 29 2024 13:08:21

%S 1,2,12,68,520,4542,46550,540136,7045020,101865410,1619046418,

%T 28053492348,526430246264,10636085523910,230214619661790,

%U 5314695463338704,130356558777712468,3385311352838750538,92797887464933030762,2677623216872061223780,81123642038690958720048

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

%H Alois P. Heinz, <a href="/A245854/b245854.txt">Table of n, a(n) for n = 1..400</a>

%F E.g.f.: 1/(2-exp(x))-1/(2-exp(x)+x).

%F a(n) = A000670(n) - A032032(n) = A245732(n,1) - A245732(n,2).

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

%p       add(b(n-j, k)*binomial(n, j), j=k..n))

%p     end:

%p a:= n-> b(n, 1) -b(n, 2):

%p seq(a(n), n=1..25);

%t 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 Column k=1 of A245733.

%Y Cf. A000670, A032032, A245732.

%K nonn

%O 1,2

%A _Alois P. Heinz_, Aug 04 2014