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%I #27 Nov 18 2015 11:48:12
%S 1,18,405,10206,275562,7794468,227988189,6839645670,209293157502,
%T 6507114533244,204974107797186,6527636971387308,209816902651734900,
%U 6798067645916210760,221786956948016376045,7279830704529008107830,240234413249457267558390,7965667386692530450620300
%N a(n) = 4*36^n*Gamma(n+3/2)/(sqrt(Pi)*(n+2)!).
%C 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.
%H Robert Israel, <a href="/A260655/b260655.txt">Table of n, a(n) for n = 0..638</a>
%F G.f.: (1/162)*(1-18*z-sqrt(1-36*z))/z^2.
%F E.g.f. (in Maple notation): (1/(9*z))*BesselI(1,18*z)*exp(18*z).
%F a(n) = 2*9^n*C(2*n+2,n)/(2*n+2) = 9^n * A000108(n+1). - _Robert Israel_, Nov 13 2015
%p seq(2*9^n*binomial(2*n+2,n)/(2*n+2), n = 0 .. 50); # _Robert Israel_, Nov 13 2015
%t 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 *)
%o (PARI) z='z+O('z^33); Vec((1/162)*(1-18*z-sqrt(1-36*z))/z^2) \\ _Altug Alkan_, Nov 13 2015
%K nonn
%O 0,2
%A _Karol A. Penson_, Nov 13 2015
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