A389384 Triangle read by rows: T(n,k) is the number of k-factors of the n-dimensional hypercube graph, 0 <= k <= n.

1, 1, 1, 1, 2, 1, 1, 9, 9, 1, 1, 272, 2970, 272, 1, 1, 589185, 2907019740, 2907019740, 589185, 1, 1, 16332454526976

Offset

0,5

Comments

T(n,k) is a multiple of binomial(n,k).

Links

Table of n, a(n) for n=0..22.

Wikipedia, Graph factorization.

Wikipedia, Hypercube graph.

Formula

T(n,k) = T(n,n-k).

Example

Triangle begins:
  n\k| 0      1          2          3      4  5
  ---+-----------------------------------------
  0  | 1
  1  | 1      1
  2  | 1      2          1
  3  | 1      9          9          1
  4  | 1    272       2970        272      1
  5  | 1 589185 2907019740 2907019740 589185  1

Crossrefs

Columns: A005271 (k=1), A389385 (k=2), A389386 (k=3).

Sequence in context: A108558 A128434 A176417 * A119731 A368928 A283321

Adjacent sequences: A389381 A389382 A389383 * A389385 A389386 A389387

Keyword

nonn,tabl,hard,more

Author

Pontus von Brömssen, Oct 03 2025

Status

approved