%I A002137 M4154 N1726
%S A002137 1,0,1,1,6,22,130,822,6202,52552,499194,5238370,60222844,752587764,
%T A002137 10157945044,147267180508,2282355168060,37655004171808,658906772228668,
%U A002137 12188911634495388,237669544014377896,4871976826254018760,104742902332392298296
%N A002137 Number of n X n symmetric matrices with positive entries, trace 0 and 
               all row sums 2.
%D A002137 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002137 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002137 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.
%D A002137 I. M. H. Etherington, Some problems of non-associative combinations, 
               Edinburgh Math. Notes, 32 (1940), 1-6.
%D A002137 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.
%D A002137 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Example 5.2.8.
%H A002137 T. D. Noe, <a href="b002137.txt">Table of n, a(n) for n=0..100</a>
%F A002137 E.g.f.: (1-x)^(-1/2)*exp(-x/2+x^2/4).
%F A002137 a(n)=(n-1)(a(n-1)+a(n-2))-(n-1)(n-2)a(n-3)/2.
%Y A002137 Cf. A000985, A000986.
%Y A002137 Sequence in context: A027296 A151495 A009358 this_sequence A009361 A075759 
               A000993
%Y A002137 Adjacent sequences: A002134 A002135 A002136 this_sequence A002138 A002139 
               A002140
%K A002137 nonn,nice,easy
%O A002137 0,5
%A A002137 N. J. A. Sloane (njas(AT)research.att.com).