A007868 Number of inverse pairs of elements in symmetric group S_n, or pairs of total orders on n nodes (average of A000085 and A000142).

1, 1, 2, 5, 17, 73, 398, 2636, 20542, 182750, 1819148, 19976248, 239570876, 3113794652, 43590340840, 653842358768, 10461418047368, 177843819947656, 3201187351520912, 60822552609266720, 1216451015967652048, 25545471145831066448, 562000364198246159456

Offset

0,3

Links

T. D. Noe, Table of n, a(n) for n=0..100

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Formula

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

a(n) ~ n! / 2. - Vaclav Kotesovec, Feb 15 2015

Mathematica

(Table[n!, {n, 0, 20}] + Range[0, 20]! CoefficientList[Series[Exp[x + x^2/2], {x, 0, 20}], x])/2  (* Geoffrey Critzer, Nov 07 2011 *)

Crossrefs

Sequence in context: A002135 A260337 A217944 * A136726 A112831 A081046

Adjacent sequences: A007865 A007866 A007867 * A007869 A007870 A007871

Keyword

nonn,nice

Author

Peter J. Cameron

Status

approved