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A291960 Triangle read by rows: T(n,k) = T(n-k,k-1) + k * T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

%I A291960 #25 Sep 07 2017 08:48:42
%S A291960 1,0,1,0,1,0,1,1,0,1,1,0,1,3,0,1,3,1,0,1,7,1,0,1,7,3,0,1,15,6,0,1,15,
%T A291960 10,1,0,1,31,16,1,0,1,31,33,3,0,1,63,45,6,0,1,63,79,14,0,1,127,130,20,
%U A291960 1,0,1,127,198,45,1,0,1,255,300,69,3,0,1,255,517,135
%N A291960 Triangle read by rows: T(n,k) = T(n-k,k-1) + k * T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).
%H A291960 Seiichi Manyama, <a href="/A291960/b291960.txt">Rows n = 0..481, flattened</a>
%F A291960 G.f. of column k: x^(k*(k+1)/2) / Product_{j=1..k} (1-j*x^j).
%e A291960 First few rows are:
%e A291960   1;
%e A291960   0, 1;
%e A291960   0, 1;
%e A291960   0, 1,  1;
%e A291960   0, 1,  1;
%e A291960   0, 1,  3;
%e A291960   0, 1,  3,  1;
%e A291960   0, 1,  7,  1;
%e A291960   0, 1,  7,  3;
%e A291960   0, 1, 15,  6;
%e A291960   0, 1, 15, 10, 1.
%Y A291960 Row sums give A204856.
%Y A291960 Columns 0-2 give A000007, A000012, A052551(n-3).
%Y A291960 Cf. A008289, A216652, A291969.
%K A291960 nonn,tabf
%O A291960 0,14
%A A291960 _Seiichi Manyama_, Sep 06 2017