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A364072
Triangle read by rows: T(n, k) = Sum_{d=0..n-k} binomial(n, d)*StirlingS2(n-d, k)*63^(n-d-k), with 0 <= k <= n.
3
1, 1, 1, 1, 65, 1, 1, 4161, 192, 1, 1, 266305, 28545, 382, 1, 1, 17043521, 3891520, 101125, 635, 1, 1, 1090785345, 511266561, 23105270, 261780, 951, 1, 1, 69810262081, 66021638592, 4901267861, 89335610, 562296, 1330, 1, 1, 4467856773185, 8454558363265, 997262532182, 27503177191, 267021146, 1066366, 1772, 1
OFFSET
0,5
COMMENTS
T(n, k) is the number of 64-subgroups of R^n which have dimension k, 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. 7-9.
EXAMPLE
The triangle begins:
1;
1, 1;
1, 65, 1;
1, 4161, 192, 1;
1, 266305, 28545, 382, 1;
1, 17043521, 3891520, 101125, 635, 1;
1, 1090785345, 511266561, 23105270, 261780, 951, 1;
...
MATHEMATICA
T[n_, k_]:=Sum[Binomial[n, d]StirlingS2[n-d, k]63^(n-d-k), {d, 0, n-k}]; Table[T[n, k], {n, 0, 8}, {k, 0, n}]//Flatten
CROSSREFS
Cf. A000012 (k=0), A133853 (k=1), A364069 (row sums), A364071, A364073.
Sequence in context: A204043 A295175 A351308 * A279290 A034061 A113696
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Jul 04 2023
STATUS
approved