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A000985 Number of n X n symmetric matrices with nonnegative entries and all row sums 2.
(Formerly M2907 N1168)
9
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; text; internal format)
OFFSET

0,3

REFERENCES

Doslic, Tomislav and Veljan, Darko. Logarithmic behavior of some combinatorial sequences. Discrete Math. 308 (2008), no. 11, 2182--2212. MR2404544 (2009j:05019) - From N. J. A. Sloane, May 01 2012

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.

LINKS

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

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 584

H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), vol 3, 653-659.

H. Gupta, >Enumeration of symmetric matrices (annotated scanned copy)

FORMULA

E.g.f.: (1-x)^(-1/2)*exp(x^2/4 + x/(2*(1-x))).

a(n) ~ n^n*exp(sqrt(2*n)-n)/sqrt(2) * (1-5/(24*sqrt(2*n))). - Vaclav Kotesovec, Jul 29 2013

Recurrence: 2*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-2)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*a(n-3) + (n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Jul 29 2013

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]! (* Jean-Fran├žois Alcover, Nov 25 2011 *)

CROSSREFS

Cf. A000986.

Sequence in context: A174627 A007841 A036760 * A207433 A094611 A052442

Adjacent sequences:  A000982 A000983 A000984 * A000986 A000987 A000988

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 24 05:48 EST 2018. Contains 299597 sequences. (Running on oeis4.)