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Search: id:A133800
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| A133800 |
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Triangle read by rows in which row n gives number of ways to partition n labeled elements into k pie slices allowing the pie to be turned over (n >= 1, 1 <= k <= n). |
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+0
3
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| 1, 1, 1, 1, 3, 1, 1, 7, 6, 3, 1, 15, 25, 30, 12, 1, 31, 90, 195, 180, 60, 1, 63, 301, 1050, 1680, 1260, 360, 1, 127, 966, 5103, 12600, 15960, 10080, 2520, 1, 255, 3025, 23310, 83412, 158760, 166320, 90720, 20160, 1, 511, 9330, 102315, 510300, 1369620
(list; table; graph; listen)
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OFFSET
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1,5
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LINKS
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C. G. Bower, Transforms (2)
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FORMULA
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Take triangle of Stirling numbers of second kind (A008277) and multiply k-th column by A001710(k) (order of altrenating group A_k).
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EXAMPLE
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Triangle begins:
1,
1,1,
1,3,1,
1,7,6,3,
1,15,25,30,12,
1,31,90,195,180,60,
1,63,301,1050,1680,1260,360,
...
For row n = 4 we have the following "pies":
. 1
./ \
2 . 3 . 12 .. 12 . 123
.\ / .. / \ .(..)..(..)
. 4 .. 3--4 . 34 .. 4 .. (1234)
k=4 .. k=3 ..k=2 . k=2 . k=1
(3)....(6)...(3)..(4)... (1)
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MAPLE
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A001710 := proc(n) if n < 2 then 1; else n!/2 ; fi ; end: A008277 := proc(n, k) combinat[stirling2](n, k) ; end: A133800 := proc(n, k) A008277(n, k)*A001710(k-1) ; end: for n from 1 to 10 do for k from 1 to n do printf("%d, ", A133800(n, k)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 18 2008
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CROSSREFS
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Row sums give A032262. Diagonals give A000225, A000392, A032263, A133799, A001710.
Sequence in context: A154959 A008277 A080417 this_sequence A146900 A132733 A082039
Adjacent sequences: A133797 A133798 A133799 this_sequence A133801 A133802 A133803
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Barry Cipra and N. J. A. Sloane (njas(AT)research.att.com), Jan 17 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 18 2008
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