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EXAMPLE
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The asymptotic behavior can be demonstrated at the 4th row function:
R_4(y) = 1 + 4*y + 9*y^2/2! + 27*y^3/3! + 16*y^4/4! + 32*y^5/5! + y^6/6! + y^7/7!;
R_4(1) = 14.93492... = (0.895684...)*r^4, where r = 2.0207473586...
Rows begin:
[1]
[1, 1],
[1, 2, 1, 1],
[1, 3, 4, 8, 1, 1],
[1, 4, 9, 27, 16, 32, 1, 1],
[1, 5, 16, 64, 81, 243, 64, 128, 1, 1],
[1, 6, 25, 125, 256, 1024, 729, 2187, 256, 512, 1, 1],
[1, 7, 36, 216, 625, 3125, 4096, 16384, 6561, 19683, 1024, 2048, 1, 1],
...
which can be derived from the square array A003992:
[1, 0, 0, 0, 0, 0, 0, ...],
[1, 1, 1, 1, 1, 1, 1, ...],
[1, 2, 4, 8, 16, 32, 64, ...],
[1, 3, 9, 27, 81, 243, 729, ...],
[1, 4, 16, 64, 256, 1024, 4096, ...],
[1, 5, 25, 125, 625, 3125, 15625, ...],
...
by shifting each column k down by floor(k/2) rows, and omitting the zeros coming from row 0 of A003992.
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