|
|
A288853
|
|
Triangle read by rows: T(n,k) is the number of surjective linear mappings from an n-dimensional vector space over F_2 onto a k-dimensional vector space, n>=0, 0<=k<=n.
|
|
2
|
|
|
1, 1, 1, 1, 3, 6, 1, 7, 42, 168, 1, 15, 210, 2520, 20160, 1, 31, 930, 26040, 624960, 9999360, 1, 63, 3906, 234360, 13124160, 629959680, 20158709760, 1, 127, 16002, 1984248, 238109760, 26668293120, 2560156139520, 163849992929280, 1, 255, 64770, 16322040, 4047865920, 971487820800, 217613271859200, 41781748196966400, 5348063769211699200
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
A022166(m,k)*T(n,k) is the number of m X n matrices over F_2 that have rank k.
a(n) is the number of n X n matrices over F_2 in Green's R class containing A where rank(A) = k. - Geoffrey Critzer, Oct 05 2022
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = Product_{j=0..k-1} (2^n - 2^j).
|
|
EXAMPLE
|
1;
1, 1;
1, 3, 6;
1, 7, 42, 168;
1, 15, 210, 2520, 20160;
1, 31, 930, 26040, 624960, 9999360;
...
|
|
MATHEMATICA
|
Table[Table[Product[q^n - q^i, {i, 0, k - 1}] /. q -> 2, {k, 0, n}], {n, 0, 8}] // Grid
|
|
CROSSREFS
|
Columns k=0-10 give: A000012, A000225, 6*A006095, 168*A006096, 20160*A006097, 9999360*A006110, 20158709760*A022189, 163849992929280*A022190, 5348063769211699200*A022191, 699612310033197642547200*A022192, 366440137299948128422802227200*A022193.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|