|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|