[seqfan] Re: about A011971

[Neil Sloane]

Roger said:
> In the notice about A011971, in the second line of comments, it is
written that if  P is the lower-triangular Pascal-matrix, then the
triangular matrix A011971 (Bell-Aitken-Peirce triangle)  is exp(P)/exp(1).
I think it is not.

Correct (as Robert Israel already said)!  In fact, exp(P)/exp(1) is the
array in A056857,
as the following crude Maple program reveals::

with(LinearAlgebra);
Digits:=20;
f:=n->[seq(binomial(n,i),i=0..5)];
e1:=evalf(exp(1));

A:=Matrix(6,6, [seq(f(i),i=0..5)]);
II:=IdentityMatrix(6);
m1:=II+add(A^i/i!,i=1..40);
m2:=map(evalf,m1/e1);
m3:=map(round,m2);

                            [ 1     0     0     0    0    0]
                            [                              ]
                            [ 1     1     0     0    0    0]
                            [                              ]
                            [ 2     2     1     0    0    0]
                      m3 := [                              ]
                            [ 5     6     3     1    0    0]
                            [                              ]
                            [15    20    12     4    1    0]
                            [                              ]
                            [52    75    50    20    5    1]


Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Apr 29, 2015 at 6:37 PM, <israel at math.ubc.ca> wrote:

> This is correct. P being a lower triangular matrix with 1's on the
> diagonal, exp(P)/exp(1) will have 1's on its diagonal, which A011971 does
> not. It looks like the first column of A011971 is the same as the first
> column of exp(P)/exp(1). I don't know what relationship, if any, exp(P) has
> to the rest of A011971.
>
> Cheers,
> Robert
>
>
> On Apr 29 2015, rcuculiere at free.fr wrote:
>
>  Good evening. In the notice about A011971, in the second line of
>> comments, it is written that if P is the lower-triangular Pascal-matrix,
>> then the triangular matrix A011971 (Bell-Aitken-Peirce triangle) is
>> exp(P)/exp(1). I think it is not. Greetings.
>>
>> Roger CUCULIÈRE
>> 35, rue d'Alsace         92110 CLICHY LA GARENNE FRANCE
>> <rcuculiere at free.fr>
>>
>>
>>
>>
>>
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