A039597

[Joshua Zucker]

What exactly is its name supposed to mean?

I have in mind from the definition an array like

n n1 n2 n3 ...
k k1 k2 k3 ...

where each n > n1 > n2 ...
and each k > k1 > k2 ...
and n > k, n1 > k1, ...

where all the entries are nonnegative integers.

But of course there are no such arrays.

I presume, then, that once ni = 0, then all the subsequent n's are 0.

But even then, isn't T(1,0) = 1, namely the array
1 0 0 0 ...
0 0 0 0 ...

but the seq gives T(1,0) = 2.

How about T(2,0)?  I can see two of those,
2 1 0 ...
0 0 0 ...

and

2 0 0 ...
0 0 0 ...

and for T(2,1) I see those same two, only with a 1 in the bottom left corner.

But the seq gives 4 and 6 for those values.

Help?

Thanks,
--Joshua Zucker