

A334689


Triangle read by rows: T(n,k) (0 <= k <= n) = k!*(Stirling2(n,k)+(k+1)*Stirling2(n,k+1))^2.


1



1, 1, 1, 1, 9, 2, 1, 49, 72, 6, 1, 225, 1250, 600, 24, 1, 961, 16200, 25350, 5400, 120, 1, 3969, 181202, 735000, 470400, 52920, 720, 1, 16129, 1866312, 17360406, 26460000, 8490720, 564480, 5040, 1, 65025, 18301250, 362237400, 1159593624, 840157920, 153679680, 6531840, 40320
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OFFSET

0,5


COMMENTS

This is the number of Boolean matrices of dimension n and rank k having a MoorePenrose inverse (KimRoush, Th. 10).
Theorem 8 of the same KimRoush paper gives a formula for the number of Boolean matrices of dimension n and rank k having a minimumnorm ginverse. Unfortunately the formula appears to produce negative numbers.


LINKS

Table of n, a(n) for n=0..44.
Ki Hang Kim, and Fred W. Roush, Inverses of Boolean matrices, Linear Algebra and its Applications 22 (1978): 247262. See Th. 10.


EXAMPLE

Triangle begins:
1,
1, 1,
1, 9, 2,
1, 49, 72, 6,
1, 225, 1250, 600, 24,
1, 961, 16200, 25350, 5400, 120,
1, 3969, 181202, 735000, 470400, 52920, 720,
1, 16129, 1866312, 17360406, 26460000, 8490720, 564480, 5040,
...


MAPLE

T := (n, k) > k!*(Stirling2(n, k)+(k+1)*Stirling2(n, k+1))^2;
r:=n>[seq(T(n, k), k=0..n)];
for n from 0 to 12 do lprint(r(n)); od:


CROSSREFS

Columns k=02 give: A000012, A060867, 2*A129839(n+1).
Row sums give A014235.
Sequence in context: A010536 A239908 A293171 * A335086 A151898 A080994
Adjacent sequences: A334686 A334687 A334688 * A334690 A334691 A334692


KEYWORD

nonn,tabl


AUTHOR

N. J. A. Sloane, May 11 2020


STATUS

approved



