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A158902 Triangle read by rows: the matrix product A051731 * A158821.

%I A158902 #16 Feb 01 2023 07:06:49
%S A158902 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 A158902 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 A158902 23,1,1,1,0,1,0,0,0,0,0,1
%N A158902 Triangle read by rows: the matrix product A051731 * A158821.
%F A158902 T(n,n) = 1.
%F A158902 T(n,1) = A158901(n).
%e A158902 First few rows of the triangle =
%e A158902 1;
%e A158902 2, 1;
%e A158902 3, 0, 1;
%e A158902 5, 1, 0, 1;
%e A158902 5, 0, 0, 0, 1;
%e A158902 9, 1, 1, 0, 0, 1;
%e A158902 7, 0, 0, 0, 0, 0, 1;
%e A158902 12, 1, 0, 1, 0, 0, 0, 1
%e A158902 11, 0, 1, 0, 0, 0, 0, 0, 1;
%e A158902 15, 1, 0, 0, 1, 0, 0, 0, 0, 1;
%e A158902 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A158902 23, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1;
%e A158902 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A158902 21, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1;
%e A158902 ...
%p A158902 A158902 := proc(n,k)
%p A158902     add( A051731(n,j)*A158821(j-1,k-1),j=k..n) ;
%p A158902 end proc:
%p A158902 seq(seq(A158902(n,k),k=1..n),n=1..12) ; # _R. J. Mathar_, Jan 08 2015
%t A158902 m = 12; (* number of rows *)
%t A158902 T1[n_, k_] := Boole[Mod[n, k] == 0];
%t A158902 T2[n_, k_] := Which[n == k, 1, k == 1, n-1, True, 0];
%t A158902 T = Array[T1, {m, m}].Array[T2, {m, m}];
%t A158902 Table[T[[n, k]], {n, m}, {k, n}] // Flatten (* _Jean-François Alcover_, Feb 01 2023 *)
%Y A158902 Cf. A158821, A051731, A158901, A000203 (row sums).
%K A158902 nonn,tabl
%O A158902 1,2
%A A158902 _Gary W. Adamson_ and _Mats Granvik_, Mar 29 2009
%E A158902 Wrong A-number in definition corrected by _Robert Israel_, Jan 08 2015