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(C++) (* ++) // see link above *)

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Shiyao Guo, <a href="/A341761/b341761.txt">Table of n, a(n) for n = 0..1890</a>

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Andrew Howroyd: ok, i see what are you doing. I think at some point it would be worth also adding the array (read by antidiagonals downwards) of the n-th polynomial evaluated at k (so A340885 is column 2)

S[n_, x_] := Total[Length /@ DeleteDuplicates /@ Subsequences /@ Tuples[Table[i, {i, 0, x}], n] - 1]; A341761[n_] := CoefficientList[FindSequenceFunction[ParallelTable[S[n, i], {i, 0, n + 1}], x], {x}]; Join[{0, 0, 1}, Table[A341761[n], {n, 2, 7}] // Flatten] (* Robert P. P. McKone, Feb 20 2021 *)

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