Column k =1 of the table is the integers, from n=1 in row 1.

The n-th row of the table is a repeating pattern, starting with the value of n followed by n instances of zero, as created by the characteristic function of the multiples of (n+1).

As table T(n,k)= n*(floor((n+k)/(n+1)-floor((n+k-1)/(n+1)).

As linear sequence a(n) = A002260(n)*(floor(A003057(n))/(A002260(n)+1)-floor(A002024(n))/(A002260(n)+1)); a(n)=i*(floor((t+2)/(i+1)-floor((t+1)/(i+1)), where i=n-t*(t+1)/2, t=floor((-1+sqrt(8*n-7))/2). (End)