[seqfan] Number of non-selfintersecting polytetrahdra

[Felix Fröhlich]

Dear SeqFans

I had the idea for the following sequence:

Number of non-selfintersecting polytetrahedra with n cells such that any
two such polytetrahedra with n cells remain invariant under rotations
and/or reflections.

>From what I could determine, the sequence seems to start (with offset 1)

1, 1, 1, 3, 15

Note that this differs from A276272.

I think this should be added to the OEIS (even though it is short), but
there is still one problem:

Does this differ from all sequences that come up when searching for 1, 1,
3, 15?

Unfortunately determining the next term seems to be difficult, as the
number of possibilities seems to increase quickly.

Does anyone know the next term?

Best regards
Felix