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Riordan arrays are an important tool in the study of sequences. See the examples on the OEIS Wiki. With Maple the computation of Riordan arrays is straightforward, here an example of an exponential Riordan array:

Riordan := (d,h,n,k) -> coeftayl(d*h^k,x=0,n)*n!/k!:
A131222 := (n,k) -> Riordan(1,log((1-x)/(1-2*x)),n,k):
seq(print(seq(A131222(n,k),k=0..n)),n=0..5);

1
0,   1
0,   3,   1
0,  14,   9,   1
0,  90,  83,  18,  1
0, 744, 870, 275, 30, 1

It is not clear to me how Riordan arrays are computed efficiently with Sage. Any hints are appreciated.