A260655 a(n) = 4*36^n*Gamma(n+3/2)/(sqrt(Pi)*(n+2)!).

1, 18, 405, 10206, 275562, 7794468, 227988189, 6839645670, 209293157502, 6507114533244, 204974107797186, 6527636971387308, 209816902651734900, 6798067645916210760, 221786956948016376045, 7279830704529008107830, 240234413249457267558390, 7965667386692530450620300

Offset

0,2

Comments

a(n) is the n-th Hausdorff moment of the semiellipse on (0,36) in the form (1/162)*sqrt(x)*sqrt(36-x)/Pi. This is a rescaled variant of Wigner's semicircle distribution.

Links

Robert Israel, Table of n, a(n) for n = 0..638

Formula

G.f.: (1/162)*(1-18*z-sqrt(1-36*z))/z^2.

E.g.f. (in Maple notation): (1/(9*z))*BesselI(1,18*z)*exp(18*z).

a(n) = 2*9^n*C(2*n+2,n)/(2*n+2) = 9^n * A000108(n+1). - Robert Israel, Nov 13 2015

Maple

seq(2*9^n*binomial(2*n+2, n)/(2*n+2), n = 0 .. 50); # Robert Israel, Nov 13 2015

Mathematica

Table[4*36^n Gamma[n + 3/2]/(Sqrt[Pi] (n + 2)!), {n, 0, 17}] (* or *) Table[2*9^n Binomial[2 n + 2, n]/(2 n + 2), {n, 0, 17}] (* Michael De Vlieger, Nov 18 2015 *)

Prog

(PARI) z='z+O('z^33); Vec((1/162)*(1-18*z-sqrt(1-36*z))/z^2) \\ Altug Alkan, Nov 13 2015

Crossrefs

Sequence in context: A111454 A116421 A298465 * A318598 A215229 A172135

Adjacent sequences: A260652 A260653 A260654 * A260656 A260657 A260658

Keyword

nonn

Author

Karol A. Penson, Nov 13 2015

Status

approved