A082042 (n^2+1)n!.

1, 2, 10, 60, 408, 3120, 26640, 252000, 2620800, 29756160, 366508800, 4869849600, 69455232000, 1058593536000, 17174123366400, 295534407168000, 5377157001216000, 103149354147840000, 2080771454361600000

Offset

0,2

Comments

Main diagonal of A082037

a(n) = total number of runs when each permutation on [n+1] is split into maximal monotone runs. (A monotone run is a sequence of consecutive entries whose differences are all 1 or all -1. Example: 34-1-765-2 contributes 4 runs to a(6) as indicated.) - David Callan, Nov 16 2003

Links

Table of n, a(n) for n=0..18.

Formula

a(n)=A002522(n)*A000142(n).

(n^2-2*n+2)*a(n) -n*(n^2+1)*a(n-1)=0. - R. J. Mathar, Dec 03 2014

Crossrefs

Cf. A018932. [From R. J. Mathar, Dec 15 2008]

Sequence in context: A262001 A276310 A098616 * A260657 A079856 A073329

Adjacent sequences: A082039 A082040 A082041 * A082043 A082044 A082045

Keyword

easy,nonn

Author

Paul Barry, Apr 02 2003

Status

approved