I've got some mail, where the author considered

the case from the view of generation-functions,

which may be interesting for a needed proof of

the method.

Here some exchange:

Next mail:

Then I did not understand, how the generation-function was

related to the bivariate array:

Final mail:

the case from the view of generation-functions,

which may be interesting for a needed proof of

the method.

Here some exchange:

Code:

`It seems that e.g.f. of your triangle is:`

(exp(y*(exp(y*(exp(x)-1))-1))-1)/y^2

which gives

1,

1,1,1,

1,3,4,3,1,

1,7,13,19,13,6,1,

...

Code:

`And the e.g.f. connected to your coefficient a_3() is`

(exp(y*(exp(y*(exp(y*(exp(x)-1))-1))-1))-1)/y^3

which gives triangle

1,

1,1,1,1,

1,3,4,6,4,3,1,

1,7,13,26,31,31,25,13,6,1,

...

And so on.

related to the bivariate array:

Code:

`´`

> However, I did not understand how you arrived

> via the generation-function process at the

> actual K-matrices. Would you mind to explain

> this to me?

>

> Gottfried

Code:

`An example:`

Substituting t = exp(y) in your U_t(x,2) we get

exp(y*(exp(y*(exp(x)-1))-1))-1 =

y^2*x+(1/2*y^2+1/2*y^3+1/2*y^4)*x^2+(1/6*y^2+1/2*y^3+2/3*y^4+1/2*y^5+1/6*y^6)*x^3+(1/24*y^2+7/24*y^3+13/24*y^4+19/24*y^5+13/24*y^6+1/4*y^7+1/24*y^8)*x^4+...

.

Gottfried Helms, Kassel