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

0,2

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.

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

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 *)

Crossrefs

Cf. A000774.

Sequence in context: A317077 A009437 A347072 * A327030 A355986 A000239

Adjacent sequences: A000773 A000774 A000775 * A000777 A000778 A000779

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Incorrect formula deleted by Mark van Hoeij, Nov 11 2009

Offset corrected by Gary Detlefs, Jul 13 2010

Status

approved