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A002137 Number of n X n symmetric matrices with positive entries, trace 0 and all row sums 2.
(Formerly M4154 N1726)
+0
3
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)
OFFSET

0,5

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.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.8.

LINKS

T. D. Noe, Table of n, a(n) for n=0..100

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.

CROSSREFS

Cf. A000985, A000986.

Sequence in context: A100300 A027296 A009358 this_sequence A009361 A075759 A000993

Adjacent sequences: A002134 A002135 A002136 this_sequence A002138 A002139 A002140

KEYWORD

nonn,nice,easy

AUTHOR

njas

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Last modified July 23 17:35 EDT 2008. Contains 142285 sequences.


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