[seqfan] Re: A182080: nice sequence needing more terms

[Maximilian Hasler]

I noticed that the given terms of https://oeis.org/A182080 :
maximal depth of an indecomposable exact cover of an n-set.
coincide with the first terms of https://oeis.org/A096753 :
"Antidiagonal sums of table A096751."
but there is no formula or program there.

Then I found that columns of https://oeis.org/A096651 :
"Lower triangular matrix T, read by rows, such that the row sums of
T^n form the n-dimensional partitions."
are the binomial transforms of rows of https://oeis.org/A096806
"Triangle, read by rows, such that the binomial transform of the n-th
row lists the m-dimensional partitions of n, for n>=1 and m>=0."

There are formulae for particular values given for these two.
I think that  the last part of
%F A096806
T(n, 0)=T(n, n-1)=1, T(n, 1)=A000041(n)-1, T(n+1,
n-1)=(n-1)*(n-2)/2+1, for n>=1.

is wrong : The given value is rather T(n,n-2)  (or change n-2 to n).

Can s/o confirm this ? (and maybe correct on OEIS ?)

If s/o has formulae and/or programs for any of these or the related
sequences (A096642-A096653, ...)
it would be nice if these were added.

Thanks in advance,

Maximilian