A000776 a(n) = n! * (1 + 2*Sum_{k=1..n} 1/k).

1, 3, 8, 28, 124, 668, 4248, 31176, 259488, 2416032, 24886080, 281004480, 3451887360, 45832538880, 654109585920, 9986000371200, 162391354675200, 2802498609254400, 51156349822771200, 984775394044108800, 19938798081699840000, 423580563732049920000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n-1) equals -1 times the coefficient of x of the characteristic polynomial of the n X n matrix whose (i,j)-entry is equal to i if i=j and is equal to 1 otherwise. - John M. Campbell, May 23 2011

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..250
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 140
• J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

Crossrefs

Cf. A000774.

Programs

Maple

a := proc(n) option remember: if(n=0)then return 1: fi: return n*a(n-1)+2*(n-1)!: end: seq(a(n),n=0..21); # Nathaniel Johnston, Jun 14 2011

Mathematica

Table[-Coefficient[CharacteristicPolynomial[Array[KroneckerDelta[#1, #2] (((#1)) - 1) + 1 &, {n, n}], x], x], {n, 1, 10}] (* John M. Campbell, May 23 2011 *)
Table[n! (1 + 2 HarmonicNumber[n]), {n, 0, 30}] (* Jean-François Alcover, Feb 11 2016 *)

Formula

E.g.f. (with offset 1): log(1-x)*(log(1-x)-1). - Vladeta Jovovic, Nov 19 2009

a(0)=1, a(n+1) = (n+1)*a(n) + 2*n!, n > 0. - Sean A. Irvine, Jun 14 2011

Extensions

Incorrect formula deleted by Mark van Hoeij, Nov 11 2009

Offset corrected by Gary Detlefs, Jul 13 2010