Missing Table?

[Paul D. Hanna]

Seqfans,
     Where is the rectangular table referred to by these sequences?
 
A040027  Main diagonal of an array of binomial recurrence coefficients.  
 0, 1, 1, 3, 9, 31, 121, 523, 2469, 12611, 69161, 404663,  
A045501  Second diagonal in table of binomial recurrence coefficients.  
 1, 1, 4, 14, 54, 233, 1101, 5625, 30846, 
A045499  Third diagonal in table of binomial recurrence coefficients. 
 1, 1, 5, 20, 85, 400, 2046, 11226, 65676, 407787, 2675410, 
A045500  Fourth diagonal in table of binomial recurrence coefficients. 
 1, 1, 6, 27, 125, 635, 3488, 20425, 126817, 831915, 5744784, 41618459 
(AUTHOR of these sequences:  H. W. Gould) 
 
The closest thing I can find is Emeric Deutsch's recent triangle A124496,

in which these sequences appear as columns. 
 
The lower half of the table (I guess) must look like this:
1, ...
1, 1, ...
1, 1, 3, ...
1, 1, 4, 9, ...
1, 1, 5, 14, 31, ...
1, 1, 6, 20, 54, 121, ...
1, 1, 7, 27, 85, 233, 523, ...
1, 1, 8, 35, 125, 400, 1101, 2469, ...
1, 1, 9, 44, 175, 635, 2046, 5625, 12611, ...
 
Is the complete table in the OEIS?  
If not, it certainly should be. 
     Paul
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