A308498 - OEIS

%I #8 Jun 01 2019 11:11:43

%S 1,2,1,6,5,1,24,27,10,1,120,168,88,17,1,720,1200,800,225,26,1,5040,

%T 9720,7800,2850,486,37,1,40320,88200,82320,36750,8232,931,50,1,362880,

%U 887040,940800,493920,136416,20384,1632,65,1,3628800,9797760,11612160,6985440

%N Triangle read by rows where T(n,k), n>=1, 1<=k<=n is the number of (0,1)-matrices of size n with the first row and column sum = k and remaining sums = 1.

%F T(n,k) = ((n-1)!)^2 * (k^2+n-k) / ((k!)^2 * (n-k)!).

%F T(n,1) = A000142(n).

%F T(n,2) = A138772(n).

%F T(n,n-1) = A002522(n-1).

%F T(n,n) = 1.

%e For n=4, k=3:

%e 1110  1101  1011  1110  1101  1011  1110  1101  1011  0111

%e 1000  1000  1000  1000  1000  1000  0001  0010  0100  1000

%e 1000  1000  1000  0001  0010  0100  1000  1000  1000  1000

%e 0001  0010  0100  1000  1000  1000  1000  1000  1000  1000

%e so T(4,3)=10.

%e Triangle begins:

%e 1

%e 2,1

%e 6,5,1

%e 24,27,10,1

%e 120,168,88,17,1

%e 720,1200,800,225,26,1

%e 5040,9720,7800,2850,486,37,1

%e 40320,88200,82320,36750,8232,931,50,1

%e 362880,887040,940800,493920,136416,20384,1632,65,1

%e 3628800,9797760,11612160,6985440,2286144,423360,44928,2673,82,1

%e 39916800,117936000,154224000,104328000,39372480,8678880,1144800,90450,4150,101,1

%Y Cf. A000142, A002522, A138772.

%K nonn,tabl

%O 1,2

%A _Lars Blomberg_, Jun 01 2019