A082042 a(n) = (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

Author

Paul Barry, Apr 02 2003

Keywords

• easy
• nonn
• changed

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

a(n) is also the number of distinct planar embeddings of the (n+1)-Sierpinski gasket graph. - Eric W. Weisstein, May 21 2024

Links

• Eric Weisstein's World of Mathematics, Planar Embedding.
• Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.

Crossrefs

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

Cf. A000142, A002522, A082037.

Formula

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

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