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A006848 Number of extreme points of the set of n X n symmetric doubly-substochastic matrices.
(Formerly M1515)
1
1, 2, 5, 18, 75, 414, 2643, 20550, 180057, 1803330, 19925541, 242749602, 3218286195, 46082917278, 710817377715, 11689297807734, 205359276208113, 3812653265319810, 75092750890627077, 1553136587207991090, 33876594618751675611, 772263699644709647262 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)