cp's OEIS Frontend

A245856 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 3.

%I A245856 #8 Feb 14 2016 11:19:11
%S A245856 1,0,0,20,70,112,1848,12840,62700,591800,5484908,40589276,421291780,
%T A245856 4704380800,46345716880,533446290384,6931113219780,85313661653400,
%U A245856 1121432682942740,16310909250477380,237534778732260548,3578871132644512672,57980168196079811800
%N A245856 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 3.
%H A245856 Alois P. Heinz, <a href="/A245856/b245856.txt">Table of n, a(n) for n = 3..400</a>
%F A245856 E.g.f.: 1/(2-exp(x)+x+x^2/2)-1/(2-exp(x)+x+x^2/2+x^3/6).
%F A245856 a(n) = A102233(n) - A232475(n) = A245732(n,3) - A245732(n,4).
%p A245856 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A245856       add(b(n-j, k)*binomial(n, j), j=k..n))
%p A245856     end:
%p A245856 a:= n-> b(n, 3) -b(n, 4):
%p A245856 seq(a(n), n=3..30);
%t A245856 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 A245856 Column k=3 of A245733.
%Y A245856 Cf. A102233, A232475, A245732.
%K A245856 nonn
%O A245856 3,4
%A A245856 _Alois P. Heinz_, Aug 04 2014