Question: Why cannot this series be ploted?

i invent a method to make use of gfun 

 

as i know series are the number of ways 

however, after i input the number of balls in each box

calculate into binomial and input into gfun, and plot the graph, the problem is value too big 

cannot plot 

however, if using the count directly as input, the graph can be ploted, however, this is not

the logic of my understanding

if input series are not binomial, what are they?

 

freq := [20,8,22,38,49,36,59,41,32,21,23];

l := [binomial(349,20), binomial(349,8),binomial(349,22),binomial(349,38),binomial(349,49),binomial(349,36),

binomial(349,59),binomial(349,41),binomial(349,32),binomial(349,21),binomial(349,23)];

sl := gfun[listtoseries](l, x, egf);

g := convert(sl, ratpoly);

g := g - subs(x=0, g); 

g := g/subs(x=1.639E47, g);

dg := diff(g, x);

motion := {diff(f(x), x) - dg*f(x) = 0};

ic := {f(0)=1};

pdf := dsolve(motion union ic);

plot(rhs(pdf), x=-5..10);

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