
COMMENTS

a(n+1) is the sum of the zero moments over all permutations of n. E.g., a(4) is [1,2,3].[0,1,2] + [1,3,2].[0,1,2] + [2,1,3].[0,1,2] + [2,3,1].[0,1,2] + [3,1,2].[0,1,2] + [3,2,1].[0,1,2] = 8 + 7 + 7 + 5 + 5 + 4 = 36.  Jon Perry, Feb 20 2004
a(n) is the number of pairs of elements (p(i),p(j)) in an npermutation such that i > j and p(i) < p(j) where j is not equal to i1. Loosely speaking, we could say: the number of inversions that are not descents. A055303 + A001286 = A001809. For example, a(3)=3 from the permutations (given in one line notation): (2,3,1), (3,1,2), (3,2,1) we have the pairs (1,2), (2,3) and (1,3) respectively.  Geoffrey Critzer, Jan 06 2013


MATHEMATICA

With[{nn=20}, Drop[CoefficientList[Series[x^3/(2(1x)^3), {x, 0, nn}], x]Range[0, nn]!, 3]] (* Harvey P. Dale, Nov 22 2012 *)
