Did you look at ZBmath : zbmath.org/authors/?q=Vogt ?

You may like to read Salvatore and Tauraso article : arxiv.org/pdf/0802.3010.pdf

One reference : Brugallé, Koseleff, Pecker, The lexicographic degree of the first two-bridge knots

There is a natural involution on Tamari intervals, namely reversal and exchange of bounds, with fixed points counted by 1, 1, 3, 4, 15, 22, 91, 140, 612, 969, 4389, 7084, 32890, 53820, ... One expects an instance of the q=-1 phenomenon for these numbers.

More generally, odd values seem to appear for indices in oeis.org/A263133 .

According to wikipedia, Henri Becquerel (with i and not y) is the son of Alexandre Edmond Becquerel. So this is not the same prize.

Maybe p=3 and p=23 would also be interesting to consider ?

And the odd Bernoulli numbers vanish, so one can remove them from the formula.

Now in the encyclopedia as oeis.org/A301871

You need distinct real roots, no ?

Maybe this is the Desnanot-Jacobi identity ? I think I have read this in Zelevinsky.