A245856 - OEIS

%I #8 Feb 14 2016 11:19:11

%S 1,0,0,20,70,112,1848,12840,62700,591800,5484908,40589276,421291780,

%T 4704380800,46345716880,533446290384,6931113219780,85313661653400,

%U 1121432682942740,16310909250477380,237534778732260548,3578871132644512672,57980168196079811800

%N Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 3.

%H Alois P. Heinz, <a href="/A245856/b245856.txt">Table of n, a(n) for n = 3..400</a>

%F E.g.f.: 1/(2-exp(x)+x+x^2/2)-1/(2-exp(x)+x+x^2/2+x^3/6).

%F a(n) = A102233(n) - A232475(n) = A245732(n,3) - A245732(n,4).

%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, 3) -b(n, 4):

%p seq(a(n), n=3..30);

%t With[{nn=30},CoefficientList[Series[1/(2-Exp[x]+x+x^2/2)-1/(2-Exp[x]+ x+ x^2/2+ x^3/6),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 14 2016 *)

%Y Column k=3 of A245733.

%Y Cf. A102233, A232475, A245732.

%K nonn

%O 3,4

%A _Alois P. Heinz_, Aug 04 2014