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Search: id:A006847
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| A006847 |
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Extreme points of set of n X n symmetric doubly-stochastic matrices.
(Formerly M1471)
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+0
2
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| 1, 1, 2, 5, 14, 58, 238, 1516, 9020, 79892, 635984, 7127764, 70757968, 949723600, 11260506056, 175400319992, 2416123951952, 42776273847184, 671238787733920, 13302324582892048, 234257439470319776, 5135062189842955616, 100292619307729965152
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from Jeffrey Shallit (shallit(AT)cs.uwaterloo.ca), Dec 05 2009: (Start)
A recurrence formula for this sequence is:
A(n) = A(n-1) + (n-1)^2*A(n-2) - ((n-1)*(n-2)/2)*A(n-3) - (n-1)*(n-2)*(n-3)*A(n-4)
This is given in Stanley, 1980, p. 180, except that there is a typographical error in Stanley's formula (corrected here). (End)
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REFERENCES
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M. Katz, On the extreme points of a certain convex polytope, J. Combin. Theory, 8 (1970), 417-423.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Differentiably finite power series, European J. Combin., 1 (1980), 175-188.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.24(b).
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FORMULA
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E.g.f.: ((1+x)/(1-x))^(1/4)*exp(1/2*x+1/2*x^2).
A(n) = A(n-1) + (n-1)^2*A(n-2) - ((n-1)*(n-2)/2)*A(n-3) - (n-1)*(n-2)*(n-3)*A(n-4) [From Jeffrey Shallit (shallit(AT)cs.uwaterloo.ca), Dec 05 2009]
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CROSSREFS
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Cf. A053553.
Sequence in context: A047136 A047042 A110043 this_sequence A008286 A049082 A158095
Adjacent sequences: A006844 A006845 A006846 this_sequence A006848 A006849 A006850
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KEYWORD
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nonn,easy,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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