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A291969 Triangle read by rows: T(n,k) = k * (T(n-k,k-1) + T(n-k,k)) with T(0,0) = 1 for 0 <= k <= A003056(n).

%I A291969 #17 Sep 07 2017 09:43:24
%S A291969 1,0,1,0,1,0,1,2,0,1,2,0,1,6,0,1,6,6,0,1,14,6,0,1,14,18,0,1,30,36,0,1,
%T A291969 30,60,24,0,1,62,96,24,0,1,62,198,72,0,1,126,270,144,0,1,126,474,336,
%U A291969 0,1,254,780,480,120,0,1,254,1188,1080,120,0,1,510,1800
%N A291969 Triangle read by rows: T(n,k) = k * (T(n-k,k-1) + T(n-k,k)) with T(0,0) = 1 for 0 <= k <= A003056(n).
%H A291969 Seiichi Manyama, <a href="/A291969/b291969.txt">Rows n = 0..481, flattened</a>
%F A291969 G.f. of column k: k! * x^(k*(k+1)/2) / Product_{j=1..k} (1-j*x^j).
%e A291969 First few rows are:
%e A291969   1;
%e A291969   0, 1;
%e A291969   0, 1;
%e A291969   0, 1,  2;
%e A291969   0, 1,  2;
%e A291969   0, 1,  6;
%e A291969   0, 1,  6,  6;
%e A291969   0, 1, 14,  6;
%e A291969   0, 1, 14, 18;
%e A291969   0, 1, 30, 36;
%e A291969   0, 1, 30, 60, 24.
%Y A291969 Row sums give A204858.
%Y A291969 Columns 0-1 give A000007, A000012.
%Y A291969 Cf. A291960.
%K A291969 nonn,tabf
%O A291969 0,8
%A A291969 _Seiichi Manyama_, Sep 07 2017