A364073 - OEIS

A364073

Triangle read by rows: T(n, k) = Sum_{d=0..n-k} binomial(n, d)*StirlingS2(n-d, k)*624^(n-d-k), with 0 <= k <= n.

1, 1, 1, 1, 626, 1, 1, 391251, 1875, 1, 1, 244531876, 2733126, 3748, 1, 1, 152832422501, 3658206250, 9753130, 6245, 1, 1, 95520264063126, 4721932028751, 21925818740, 25346895, 9366, 1, 1, 59700165039453751, 5993213367973125, 45788990528771, 85217015555, 54578181, 13111, 1

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OFFSET

0,5

COMMENTS

T(n, k) is the number of 625-subgroups of R^n which have dimension k, where R^n is a near-vector space over a proper nearfield R.

LINKS

Table of n, a(n) for n=0..35.

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, 626, 1;