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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

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)

Tomislav Došlic, Darko Veljan, 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

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-François Alcover, Nov 25 2011 *)

CROSSREFS

Cf. A000986.

Sequence in context: A302147 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 December 4 04:22 EST 2020. Contains 338921 sequences. (Running on oeis4.)