A053553 Extreme points of set of n X n symmetric substochastic matrices.

1, 2, 5, 15, 51, 204, 933, 5115, 32385, 245214, 2090961, 20648547, 221781915, 2679261840, 34419818241, 488332067679, 7271691132033, 118162937240730, 1998172269602685, 36552556172242359, 691550102624919651, 14056929989746659252

Offset

0,2

References

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.25(b).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

E.g.f.: ((1+x)/(1-x))^(1/4) * exp(x*(3 + x)/2).

a(n) ~ n! * 2^(-1/4)*Gamma(3/4)*exp(2)/(Pi*n^(3/4)). - Vaclav Kotesovec, Aug 13 2013

Recurrence: 2*a(n) = 4*a(n-1) + 2*(n-1)^2*a(n-2) - 3*(n-2)*(n-1)*a(n-3) - 2*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Aug 13 2013

Mathematica

max = 30; f[x_]:= ((1+x)/(1-x))^(1/4)*Exp[x*(3+x)/2]; CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Nov 30 2011 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace( ((1+x)/(1-x))^(1/4)*exp(x*(3 + x)/2) )) \\ G. C. Greubel, May 16 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( ((1+x)/(1-x))^(1/4)*Exp(x*(3+x)/2) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 16 2019
(Sage) m = 30; T = taylor(((1+x)/(1-x))^(1/4)*exp(x*(3+x)/2), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 16 2019

Crossrefs

Cf. A006847.

Sequence in context: A001681 A343665 A192553 * A276721 A287583 A287276

Adjacent sequences: A053550 A053551 A053552 * A053554 A053555 A053556

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jan 16 2000

Status

approved