A308498 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.

1, 2, 1, 6, 5, 1, 24, 27, 10, 1, 120, 168, 88, 17, 1, 720, 1200, 800, 225, 26, 1, 5040, 9720, 7800, 2850, 486, 37, 1, 40320, 88200, 82320, 36750, 8232, 931, 50, 1, 362880, 887040, 940800, 493920, 136416, 20384, 1632, 65, 1, 3628800, 9797760, 11612160, 6985440

Offset: 1

Author

Lars Blomberg, Jun 01 2019

Keywords

• nonn
• tabl

Examples

			For n=4, k=3:
1110  1101  1011  1110  1101  1011  1110  1101  1011  0111
1000  1000  1000  1000  1000  1000  0001  0010  0100  1000
1000  1000  1000  0001  0010  0100  1000  1000  1000  1000
0001  0010  0100  1000  1000  1000  1000  1000  1000  1000
so T(4,3)=10.
Triangle begins:
1
2,1
6,5,1
24,27,10,1
120,168,88,17,1
720,1200,800,225,26,1
5040,9720,7800,2850,486,37,1
40320,88200,82320,36750,8232,931,50,1
362880,887040,940800,493920,136416,20384,1632,65,1
3628800,9797760,11612160,6985440,2286144,423360,44928,2673,82,1
39916800,117936000,154224000,104328000,39372480,8678880,1144800,90450,4150,101,1
		

Crossrefs

Cf. A000142, A002522, A138772.

Formula

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

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

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

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

T(n,n) = 1.