A006157 a(n+1) = (n-1)*a(n) + n*n!. (Formerly M3950)

1, 5, 28, 180, 1320, 10920, 100800, 1028160, 11491200, 139708800, 1836172800, 25945920000, 392302310400, 6320426112000, 108101081088000, 1956280854528000, 37347179950080000, 750144785854464000, 15813863053148160000, 349121438173347840000

Offset

2,2

Comments

Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1 and 321, where the ascending runs of length at least 2 are shown between parentheses. - Emeric Deutsch and Ira M. Gessel, Sep 07 2004

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=2..21.

J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62.

J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62. (Annotated scanned copy)

Formula

a(n) = (2n-1)/6 * n!.

E.g.f.: x^2*(3-x)/(6*(1-x)^2). - Emeric Deutsch and Ira M. Gessel, Sep 07 2004

Mathematica

Table[(2n-1)/6*n!, {n, 2, 30}] (* Harvey P. Dale, Jan 06 2014 *)

Crossrefs

Cf. A014484.

Sequence in context: A020081 A095676 A324352 * A179326 A156629 A331797

Adjacent sequences: A006154 A006155 A006156 * A006158 A006159 A006160

Keyword

nonn,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Harvey P. Dale, Jan 06 2014

Status

approved