A373344 -id:A373344 - cp's OEIS frontend

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A373343 Array read by ascending antidiagonals: A(n,k) is the number of cyclic de Bruijn sequences of order k and alphabet of size n, with k > 0.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 6, 24, 2, 1, 24, 20736, 373248, 16, 1, 120, 995328000, 189321481108517289984, 12635683568857645056, 2048, 1

Offset: 1

Stefano Spezia, Jun 01 2024

The 7th antidiagonal is too large to be included in Data.

			The array begins:
  1,  1,      1,                    1, ...
  1,  1,      2,                   16, ...
  2, 24, 373248, 12635683568857645056, ...
  ...

D. Condon, Yuxin Wang, and E. Yang, De Bruijn Polyominoes, arXiv:2405.18543 [math.CO], 2024. See page 5.
T. van Aardenne-Ehrenfest and N. G. de Brujin, Circuits and Trees in Oriented Linear Graphs. In: Simon Stevin 28 (1951), pp. 203-217.

Cf. A000012 (n=1), A000142 (k=1), A003992, A016031 (n=2), A373341 (acyclic), A373344 (antidiagonal sums).

A[n_,k_]:=(n!)^(n^(k-1))/n^k; Table[A[n-k+1,k],{n,6},{k,n}]//Flatten

A(n,k) = (n!)^(n^(k-1))/n^k.

A(n,k) = A373341(n,k)/A003992(n,k).

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