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Search: id:A002137
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| A002137 |
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Number of n X n symmetric matrices with positive entries, trace 0 and all row sums 2.
(Formerly M4154 N1726)
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+0
3
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| 1, 0, 1, 1, 6, 22, 130, 822, 6202, 52552, 499194, 5238370, 60222844, 752587764, 10157945044, 147267180508, 2282355168060, 37655004171808, 658906772228668, 12188911634495388, 237669544014377896, 4871976826254018760, 104742902332392298296
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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A. C. Aitken, On the number of distinct terms in the expansion of symmetric and skew determinants, Edinburgh Math. Notes, No. 34 (1944), 1-5.
I. M. H. Etherington, Some problems of non-associative combinations, Edinburgh Math. Notes, 32 (1940), 1-6.
P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.8.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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E.g.f.: (1-x)^(-1/2)*exp(-x/2+x^2/4).
a(n)=(n-1)(a(n-1)+a(n-2))-(n-1)(n-2)a(n-3)/2.
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CROSSREFS
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Cf. A000985, A000986.
Sequence in context: A100300 A027296 A009358 this_sequence A009361 A075759 A000993
Adjacent sequences: A002134 A002135 A002136 this_sequence A002138 A002139 A002140
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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