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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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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.8.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
| 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
| Cf. A000985, A000986.
Sequence in context: A151495 A193463 A009358 * A009361 A193445 A075759
Adjacent sequences: A002134 A002135 A002136 * A002138 A002139 A002140
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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