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COMMENT
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Comments from R. J. Mathar, Oct 31 2006:
This sequence provides the seeds for the construction of columns (vertical recurrence)
of A122510 insofar as each row of A123937 provides two sides of auxiliary arrays
b(.,.,.) from which a column of A122510 emerges as the third side:
A122510(d,n)=b(0,d,n) [with an auxiliary, virtual A122510(0,n)=1].
Seeds to construct two sides of b(.,.,.):
b(x,0,n)=A123937(n,x) for x<=n; b(n,y,n)=A123937(n,n) for y>=0.
Recurrence within the b(.,.,.) : b(x,y,n)=b(x,y-1,n)+b(x+1,y-1,n) for x<n.
Graphical support as if the array were built top-down and left-to-right from the seeds:
Triangle stump ("stump" means cut-off/finiteness at the bottom and top)
...................b(n,0,n)...b(n,1,n)...b(n,2,n)....
..............................
.............b(2,0,n)...b(2,1,n)....
.........b(1,0,n)...b(1,1,n)....
...b(0,0,n)..b(0,1,n)...b(0,2,n)....
equals triangle stump (note that the top line is constant) T(x,y)=A123937(x,y)
...................T(n,n)...T(n,n)...T(n,n)....
..............................
.............T(n,2).....b(2,1,n)....
.........T(n,1).....b(1,1,n)....
...T(n,0)....b(0,1,n)...b(0,2,n)....
equals triangle stump
...................T(n,n)...T(n,n)...T(n,n)....
..............................
.............T(n,2).....b(2,1,n)....
.........T(n,1).....b(1,1,n)....
...T(n,0)...A122510(1,n).A122510(2,n).A122510(3,n)....
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