cp's OEIS Frontend

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.

%I A308498 #8 Jun 01 2019 11:11:43
%S A308498 1,2,1,6,5,1,24,27,10,1,120,168,88,17,1,720,1200,800,225,26,1,5040,
%T A308498 9720,7800,2850,486,37,1,40320,88200,82320,36750,8232,931,50,1,362880,
%U A308498 887040,940800,493920,136416,20384,1632,65,1,3628800,9797760,11612160,6985440
%N 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.
%F A308498 T(n,k) = ((n-1)!)^2 * (k^2+n-k) / ((k!)^2 * (n-k)!).
%F A308498 T(n,1) = A000142(n).
%F A308498 T(n,2) = A138772(n).
%F A308498 T(n,n-1) = A002522(n-1).
%F A308498 T(n,n) = 1.
%e A308498 For n=4, k=3:
%e A308498 1110  1101  1011  1110  1101  1011  1110  1101  1011  0111
%e A308498 1000  1000  1000  1000  1000  1000  0001  0010  0100  1000
%e A308498 1000  1000  1000  0001  0010  0100  1000  1000  1000  1000
%e A308498 0001  0010  0100  1000  1000  1000  1000  1000  1000  1000
%e A308498 so T(4,3)=10.
%e A308498 Triangle begins:
%e A308498 1
%e A308498 2,1
%e A308498 6,5,1
%e A308498 24,27,10,1
%e A308498 120,168,88,17,1
%e A308498 720,1200,800,225,26,1
%e A308498 5040,9720,7800,2850,486,37,1
%e A308498 40320,88200,82320,36750,8232,931,50,1
%e A308498 362880,887040,940800,493920,136416,20384,1632,65,1
%e A308498 3628800,9797760,11612160,6985440,2286144,423360,44928,2673,82,1
%e A308498 39916800,117936000,154224000,104328000,39372480,8678880,1144800,90450,4150,101,1
%Y A308498 Cf. A000142, A002522, A138772.
%K A308498 nonn,tabl
%O A308498 1,2
%A A308498 _Lars Blomberg_, Jun 01 2019