0,3

The number of rank-orderings of (>=2)-element subsets of an n-set. (Counts nontrivial votes in a rank-ordering voting system.). E.g. a(5) = 320 = 120+120+60+20 because of 5-, 4-, 3-, and 2-element subsets. - Warren D. Smith (wds(AT)math.temple.edu), Jul 06 2005

a(n) is the number of simple cycles through a vertex of the complete graph K_(n+1) on n+1 vertices [Hassani]. For example, in the complete graph K_4 with vertex set {A,B,C,D} there are a(3) = 12 simple cycles at the vertex A, namely the six 3-cycles ABCA, ABDA, ACBA, ACDA, ADBA and ADCA and the six 4-cycles ABCDA, ABDCA, ACBDA, ACDBA, ADBCA and ADCBA. The sum of the lengths of the cycles at a vertex of K_n is equal to A141834(n). - Peter Bala (pbala(AT)toucansurf.com), Jul 09 2008

See A000522 for the number of paths between a pair of distinct vertices of K_n. - Peter Bala (pbala(AT)toucansurf.com), Jul 09 2008

Index entries for sequences related to factorial numbers

Mehdi Hassani, Counting and computing by e

a(n) = floor(n!*exp(1))-n-1, n>0. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 25 2001

Cf. A000522.

A007526(n) - n.

Sequence in context: A094434 A001574 A074445 this_sequence A061834 A082688 A099996

Cf. A141834.

Adjacent sequences: A038151 A038152 A038153 this_sequence A038155 A038156 A038157

nonn

njas