login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A334689 Triangle read by rows: T(n,k) (0 <= k <= n) = k!*(Stirling2(n,k)+(k+1)*Stirling2(n,k+1))^2. 1

%I #20 May 11 2020 11:22:03

%S 1,1,1,1,9,2,1,49,72,6,1,225,1250,600,24,1,961,16200,25350,5400,120,1,

%T 3969,181202,735000,470400,52920,720,1,16129,1866312,17360406,

%U 26460000,8490720,564480,5040,1,65025,18301250,362237400,1159593624,840157920,153679680,6531840,40320

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

%C This is the number of Boolean matrices of dimension n and rank k having a Moore-Penrose inverse (Kim-Roush, Th. 10).

%C Theorem 8 of the same Kim-Roush paper gives a formula for the number of Boolean matrices of dimension n and rank k having a minimum-norm g-inverse. Unfortunately the formula appears to produce negative numbers.

%H Ki Hang Kim, and Fred W. Roush, <a href="https://doi.org/10.1016/0024-3795(78)90075-7">Inverses of Boolean matrices</a>, Linear Algebra and its Applications 22 (1978): 247-262. See Th. 10.

%e Triangle begins:

%e 1,

%e 1, 1,

%e 1, 9, 2,

%e 1, 49, 72, 6,

%e 1, 225, 1250, 600, 24,

%e 1, 961, 16200, 25350, 5400, 120,

%e 1, 3969, 181202, 735000, 470400, 52920, 720,

%e 1, 16129, 1866312, 17360406, 26460000, 8490720, 564480, 5040,

%e ...

%p T := (n,k) -> k!*(Stirling2(n,k)+(k+1)*Stirling2(n,k+1))^2;

%p r:=n->[seq(T(n,k),k=0..n)];

%p for n from 0 to 12 do lprint(r(n)); od:

%Y Columns k=0-2 give: A000012, A060867, 2*A129839(n+1).

%Y Row sums give A014235.

%K nonn,tabl

%O 0,5

%A _N. J. A. Sloane_, May 11 2020

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)