OFFSET
2,3
COMMENTS
A(m, n) is the number of all ((m+1)^m)-subgroups of R^n, where R^n is a near-vector space over a proper nearfield R.
LINKS
Prudence Djagba and Jan Hązła, Combinatorics of subgroups of Beidleman near-vector spaces, arXiv:2306.16421 [math.RA], 2023. See pp. 7-8.
EXAMPLE
The array begins:
1, 2, 12, 120, 1424, 19488, ...
1, 2, 67, 4355, 295234, 21036803, ...
1, 2, 628, 393128, 247268752, 156500388128, ...
1, 2, 7779, 60497283, 470668752866, 3663682367243907, ...
...
MATHEMATICA
A[m_, n_]:=Sum[Sum[Binomial[n, d]StirlingS2[n-d, i](m^(m-1)-1)^(n-d-i), {d, 0, n-i}], {i, 0, n}]; Table[A[m-n+1, n], {m, 2, 10}, {n, 0, m-2}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Jul 04 2023
STATUS
approved