Search: id:A000986
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%I A000986 M3548 N1437
%S A000986 1,0,1,4,18,112,820,6912,66178,708256,8372754,108306280,1521077404,
%T A000986 23041655136,374385141832,6493515450688,119724090206940,2337913445039488,
%U A000986 48195668439235612,1045828865817825264,23826258064972682776,568556266922455167040
%N A000986 Number of n X n symmetric matrices with (0,1) entries and all row sums 
               2.
%D A000986 H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), 
               653-659.
%D A000986 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000986 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000986 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Example 5.2.8.
%D A000986 Tan and S. Gao, Enumeration of (0,1)-Symmetric Matrices,submitted [From 
               Shanzhen Gao (sgao2(AT)fau.edu), Jun 05 2009]
%H A000986 T. D. Noe, <a href="b000986.txt">Table of n, a(n) for n=0..100</a>
%F A000986 E.g.f.: (1-x)^(-1/2)*exp(-x-x^2/4 + x/((2*(1-x)))).
%F A000986 $\dsum\limits_{a_{1}=0}^{n}\dsum\limits_{c=0}^{\min \{a_{1},n-a_{1}\}}\dsum\limits_{b=0}^{\lfloor 
               (n-a_{1}-c)/2\rfloor }\frac{% (-1)^{(n-a_{1}-2b-c)+b}n!(2a_{1})!}{% 
               2^{n+a_{1}-2c}a_{1}!(n-a_{1}-2b-c)!b!(2c)!(a_{1}-c)!}$ [From Shanzhen 
               Gao (sgao2(AT)fau.edu), Jun 05 2009]
%Y A000986 Cf. A000985.
%Y A000986 Sequence in context: A060223 A144085 A003708 this_sequence A143920 A113356 
               A062805
%Y A000986 Adjacent sequences: A000983 A000984 A000985 this_sequence A000987 A000988 
               A000989
%K A000986 nonn,nice,easy
%O A000986 0,4
%A A000986 N. J. A. Sloane (njas(AT)research.att.com).

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