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A053553 Extreme points of set of n X n symmetric substochastic matrices. 2
1, 2, 5, 15, 51, 204, 933, 5115, 32385, 245214, 2090961, 20648547, 221781915, 2679261840, 34419818241, 488332067679, 7271691132033, 118162937240730, 1998172269602685, 36552556172242359, 691550102624919651, 14056929989746659252 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A201168 A001681 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

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)