HELP! A038207 analogue

[lajos66 at t-online.hu]

Please HELP!

If (2^m)

analogue:

VARIACIONES con repetición VR =n^m


A007318  	 	 Pascal's triangle read by rows: C(n,k) =
binomial(n,k) = n!/(k!*(n-k)!), 0<=k<=n. 



If (3^m)
analogue:

VARIACIONES con repetición VR =n^m

A038207  	 	 Triangle whose (i,j)-th entry is
binomial(i,j)*2^(i-j).


If (4^m) 
analogue:

VARIACIONES con repetición VR =n^m

A027465  	 	 Cube of lower triangular normalized binomial
matrix.


If  (5^m) 
analogue:

VARIACIONES con repetición VR =n^m

A038231  	 	 Triangle whose (i,j)-th entry is
binomial(i,j)*4^(i-j).



If (6^m) then 

analogue:

VARIACIONES con repetición VR =n^m

A038243  	 	 Triangle whose (i,j)-th entry is
binomial(i,j)*5^(i-j)*1^j.

If (7^m) then 

analogue:

VARIACIONES con repetición VR =n^m

No triangle!

This is sequence
A053469  	 	 A second order recursive relation.

1, 12, 108, 864, 6480, 46656, 326592, 2239488, 15116544,
100776960…

(1 fixed points  Zerinvary)

MAPLE: for i from 0 to 12 do seq(binomial(i, j)*6^(i-j), j =
0 .. i)  od;#

                                  1
                                 6, „1”
                              36, „12”, 1
                           216, „108”, 18, 1
                        1296, „864”, 216, 24, 1
                     7776, „6480”, 2160, 360, 30, 1
                46656, „46656”, 19440, 4320, 540, 36, 1
           279936, „326592”, 163296, 45360, 7560, 756, 42, 1
     1679616, „2239488”, 1306368, 435456, 90720, 12096,
1008, 48, 1

Analogue: A000240  Rencontres numbers: permutations with
exactly one fixed point.


All triangle (A007318,  A038207, A027465, A038231,
A038243  	 	 	  analogue:  (no repetition!!!!) permutations:

A008290  	 	 Triangle T(n,k) of rencontres numbers (number
of permutations of n elements with k fixed points).

If

(8^m) then 

analogue:

VARIACIONES con repetición VR =n^m

MAPLE

for i from 0 to 9 do seq(binomial(i, j)*7^(i-j), j = 0 .. i)
 od;# 
                                  1
                                 7, 1
                              49, 14, 1
                           343, 147, 21, 1
                        2401, 1372, 294, 28, 1
                    16807, 12005, 3430, 490, 35, 1
               117649, 100842, 36015, 6860, 735, 42, 1
          823543, 823543, 352947, 84035, 12005, 1029, 49, 1
    5764801, 6588344, 3294172, 941192, 168070, 19208, 1372,
56, 1

This is numbers name? 343 free fixed points, 147 one fixed
points, 21 two fixed points, 1 three fixed points

Or

343 free (0)matching numbers, 147 one (1) matching numbers,
21 two (2) matching numbers, 1 three (3) matching numbers 


fixed points?
matching numbers?

Example:
A059056  	 Penrice Christmas gift numbers, Card-matching
numbers (Dinner-Diner matching numbers).


Thanks

Zerinvary Lajos