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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Incorrect formula deleted by Mark van Hoeij, Nov 11 2009
Offset corrected by Gary Detlefs, Jul 13 2010
STATUS
approved