Discrepancy in the number of simplices in the barycentric subdivision of an $n$-simplex

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According to OEIS, the number of simplices in the barycentric subdivision of an $n$-simplex is either given by the sequence:

  1. (A002050): 1, 5, 25, 149, 1081, 9365, 94585, 1091669, 14174521, 204495125, etc.; OR
  2. (A005461): 1, 15, 180, 2100, 25200, 317520, 4233600, 59875200, 898128000, etc.

Despite them both having the description "Number of simplices in barycentric subdivision of $n$-simplex," these appear to be very different sequences.

However, I don't immediately see why this is the case, seeing as the terms of the sequences appear to differ by quite a lot. What is causing the difference in these two sequences, and is one of them more "correct" than the other?