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A006848 Number of extreme points of the set of n X n symmetric doubly-substochastic matrices.
(Formerly M1515)
1

%I M1515

%S 1,2,5,18,75,414,2643,20550,180057,1803330,19925541,242749602,

%T 3218286195,46082917278,710817377715,11689297807734,205359276208113,

%U 3812653265319810,75092750890627077,1553136587207991090,33876594618751675611,772263699644709647262

%N Number of extreme points of the set of n X n symmetric doubly-substochastic matrices.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Gheorghe Coserea, <a href="/A006848/b006848.txt">Table of n, a(n) for n = 0..200</a>

%H Simon Plouffe, Master's Thesis, Uqam 1992, <a href="http://arxiv.org/abs/0911.4975">Approximations of generating functions and a few conjectures</a>, arXiv:0911.4975 [math.NT], 2009.

%H R. P. Stanley, <a href="http://dx.doi.org/10.1016/S0195-6698(80)80051-5">Differentiably finite power series</a>, European J. Combin., 1 (1980), 175-188.

%F The lgdegf is (2+x+x^4+x^5-2*x^3-2*x^2)/(x-1)^2/(x+1)^2, conjectured in Simon Plouffe's Master's Thesis, Uqam 1992. Lgdegf is the logarithmic derivative of f(x), the g.f. is exponential.

%t Range[0, 21]! CoefficientList[Series[((1 + x)/(1 - x))^(1/4) Exp[(x (x^3 + 2 x^2 - x - 3))/(2 (x - 1) (x + 1))], {x, 0, 21}], x] (* _Vincenzo Librandi_, Aug 02 2015 *)

%o (PARI) Vec(serlaplace(((1+x)/(1-x))^(1/4) * exp((x*(x^3 + 2*x^2 - x - 3))/(2*(x-1)*(x+1)))) + O(x^33)) \\ _Gheorghe Coserea_, Aug 03 2015

%K nonn

%O 0,2

%A _N. J. A. Sloane_

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Last modified February 18 10:32 EST 2019. Contains 320250 sequences. (Running on oeis4.)