Fourth column (m=3) of triangle
A090441.
G.f. of hypergeometric type: Sum_{n>=0} a(n)*z^n/(n!)^3 = (1+2*z)/(1-z)^4;
integral representation as n-th moment of a positive function w(x) on a positive half-axis (solution of the Stieltjes moment problem), in Maple notation:
a(n) = Integral_{x=0..oo} x^n*w(x), n>=0 where w(x) = MeijerG([[],[]],[[2,1,0],[]],x)/2, w(0) = 1/2, lim_{x->oo} w(x) = 0. w(x) is monotonically decreasing over (0,infinity). The Meijer G function above cannot be represented by any other known special function.
This solution of the Stieltjes moment problem is not unique.
Asymptotics: a(n)->(1/32)*Pi^(3/2)*sqrt(2)*(32*n^2+136*n+193)*exp(-3*n)*(n)^(5/2+3*n), for n->infinity. (End)
