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

1, 2, 5, 18, 75, 414, 2643, 20550, 180057, 1803330, 19925541, 242749602, 3218286195, 46082917278, 710817377715, 11689297807734, 205359276208113, 3812653265319810, 75092750890627077, 1553136587207991090, 33876594618751675611, 772263699644709647262

Offset

0,2

References

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

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..200

Simon Plouffe, Master's Thesis, Uqam 1992, Approximations of generating functions and a few conjectures, arXiv:0911.4975 [math.NT], 2009.

R. P. Stanley, Differentiably finite power series, European J. Combin., 1 (1980), 175-188.

Formula

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.

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A319121 A289655 A189281 * A208968 A338179 A206293

Adjacent sequences: A006845 A006846 A006847 * A006849 A006850 A006851

Keyword

nonn

Author

N. J. A. Sloane

Status

approved