[seqfan] 2,5,8,11,23, then what?

[Neil Sloane]

Dear Seqfans,
In this paper on page 31 there is a sequence 2 5 8 11 23 ... which needs
more terms:

Vladimir Shevelev, On the Basis Polynomials in the Theory of Permutations
with Prescribed Up-Down Structure, arXiv|math.CO/0801.0072.

It appears that this is not yet in the OEIS. Maybe someone could extend it?

There is also an irregular triangle of coefficients in the Appendix, which
(correcting an obvious error) I have made into https://oeis.org/A263848.
This needs checking and could use more terms.