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A038154
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n!*Sum(1/k!, k=0..n-2).
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4
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0, 0, 2, 12, 60, 320, 1950, 13692, 109592, 986400, 9864090, 108505100, 1302061332, 16926797472, 236975164790, 3554627472060, 56874039553200, 966858672404672, 17403456103284402, 330665665962403980, 6613313319248079980, 138879579704209680000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
a(n) = n*a(n-1) + A000217(n-1), where A000217(n) is the n'th triangular number [From Gary Detlefs (gdetlefs(AT)aol.com), May 20 2010]
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LINKS
| Index entries for sequences related to factorial numbers
Mehdi Hassani, Counting and computing by e
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FORMULA
| a(n) = floor(n!*exp(1))-n-1, n>0. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 25 2001
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EXAMPLE
| 0=1*0+0, 2=2*0+2, 12=3*2+6, 60=4*12+12,320 = 5*60+20... [From Gary Detlefs (gdetlefs(AT)aol.com), May 20 2010]
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CROSSREFS
| Cf. A000522.
A007526(n) - n.
Cf. A141834.
Sequence in context: A094434 A001574 A074445 * A061834 A190425 A145630
Adjacent sequences: A038151 A038152 A038153 * A038155 A038156 A038157
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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