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

Meeussen Wouter (bkarnd) wouter.meeussen at vandemoortele.com
Thu Apr 12 09:57:20 CEST 2012

```Maximilian,

lots of stuff in  Suresh Govindarajan's  http://arxiv.org/abs/1203.4419

the diagonals of A096651 continue from https://oeis.org/A096651/a096651.txt as
(fill in the rising powers of n ..)
T(n+10, n) =
{1860848640+ 1143155088*n^1 -1585056060*n^2 -1928713528, -320158629, 433339347, 298270350, 85688178, 12268179, 721315 n^9}/362880
T(n+11, n) =
{-176069376000 -141334956000*n^1+ 132734456136, 209265919380, 62756096570, -35525520135, -35695700187, -13221432630, -2617399920, -276148215, -12310199*n^10}/3628800
T(n+12, n) =
{21561059520000+ 20863088311680*n^1 -13866313301280, -28168890957284, -11578276735740, 3188776522965, 5046950847015, 2293829022738, 569772522990, 83088964805, 6720583815, 234615096*n^11}/39916800
T(n+13, n) =
{-3323672352000000  -3675487509492480*n^1 + 1728650439155232, 4631274406190520, 2358077857447180, -255620343818070, -843415275224929, -457267886542170, -135043410595665, -24559118253450, -2755274780203, -176113857150, -4939227215*n^12}/479001600

No general formula as yet.
I hope you find a match with this continuation of https://oeis.org/A096753
{1,2,3,5,9,18,38,85,198,478,1192,3063,8093,21956,61087,174084,507610,1513059,4606325,14311097,45340583,146385377,481311102,1610691081,5482963115,18976210547,66739571441,238417886719}

I would apply to Paul D. Hanna for maintenance of the sequences derived from the first 14 or so rows of the Hanna triangle A096651 known mid 2004.

'Nice ones' exact a toll... (grin)

Wouter.

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Maximilian Hasler
Sent: donderdag 12 april 2012 6:55
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A182080: nice sequence needing more terms

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.

Maximilian

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