%I #16 Feb 01 2023 07:06:49

%S 1,2,1,3,0,1,5,1,0,1,5,0,0,0,1,9,1,1,0,0,1,7,0,0,0,0,0,1,12,1,0,1,0,0,

%T 0,1,11,0,1,0,0,0,0,0,1,15,1,0,0,1,0,0,0,0,1,11,0,0,0,0,0,0,0,0,0,1,

%U 23,1,1,1,0,1,0,0,0,0,0,1

%N Triangle read by rows: the matrix product A051731 * A158821.

%F T(n,n) = 1.

%F T(n,1) = A158901(n).

%e First few rows of the triangle =

%e 1;

%e 2, 1;

%e 3, 0, 1;

%e 5, 1, 0, 1;

%e 5, 0, 0, 0, 1;

%e 9, 1, 1, 0, 0, 1;

%e 7, 0, 0, 0, 0, 0, 1;

%e 12, 1, 0, 1, 0, 0, 0, 1

%e 11, 0, 1, 0, 0, 0, 0, 0, 1;

%e 15, 1, 0, 0, 1, 0, 0, 0, 0, 1;

%e 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 23, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1;

%e 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 21, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1;

%e ...

%p A158902 := proc(n,k)

%p add( A051731(n,j)*A158821(j-1,k-1),j=k..n) ;

%p end proc:

%p seq(seq(A158902(n,k),k=1..n),n=1..12) ; # _R. J. Mathar_, Jan 08 2015

%t m = 12; (* number of rows *)

%t T1[n_, k_] := Boole[Mod[n, k] == 0];

%t T2[n_, k_] := Which[n == k, 1, k == 1, n-1, True, 0];

%t T = Array[T1, {m, m}].Array[T2, {m, m}];

%t Table[T[[n, k]], {n, m}, {k, n}] // Flatten (* _Jean-François Alcover_, Feb 01 2023 *)

%Y Cf. A158821, A051731, A158901, A000203 (row sums).

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_ and _Mats Granvik_, Mar 29 2009

%E Wrong A-number in definition corrected by _Robert Israel_, Jan 08 2015