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A000985
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Number of n X n symmetric matrices with nonnegative entries and all row sums 2.
(Formerly M2907 N1168)
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7
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1, 1, 3, 11, 56, 348, 2578, 22054, 213798, 2313638, 27627434, 360646314, 5107177312, 77954299144, 1275489929604, 22265845018412, 412989204564572, 8109686585668956, 168051656468233972, 3664479286118269972, 83868072451846938336, 2009964340465840802576
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), 653-659.
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 5.2.7.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 584
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FORMULA
| E.g.f.: (1-x)^(-1/2)*exp(x^2/4 + x/(2*(1-x))).
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MATHEMATICA
| max = 21; egf[x_] := (1-x)^(-1/2)*Exp[x^2/4 + x/(2*(1-x))]; CoefficientList[ Series[ egf[x], {x, 0, max}], x]*Range[0, max]! (* From Jean-François Alcover, Nov 25 2011 *)
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CROSSREFS
| Cf. A000986.
Sequence in context: A174627 A007841 A036760 * A094611 A052442 A180112
Adjacent sequences: A000982 A000983 A000984 * A000986 A000987 A000988
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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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