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A291968 Triangle read by rows: T(n,k) = (k+1) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

%I A291968 #20 Sep 07 2017 09:29:12
%S A291968 1,0,2,0,2,0,2,6,0,2,6,0,2,12,0,2,12,24,0,2,18,24,0,2,18,48,0,2,24,72,
%T A291968 0,2,24,96,120,0,2,30,120,120,0,2,30,168,240,0,2,36,192,360,0,2,36,
%U A291968 240,600,0,2,42,288,720,720,0,2,42,336,1080,720,0,2,48,384
%N A291968 Triangle read by rows: T(n,k) = (k+1) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).
%H A291968 Seiichi Manyama, <a href="/A291968/b291968.txt">Rows n = 0..481, flattened</a>
%F A291968 G.f. of column k: (k+1)! * x^(k*(k+1)/2) / Product_{j=1..k} (1-x^j).
%e A291968 First few rows are:
%e A291968   1;
%e A291968   0, 2;
%e A291968   0, 2;
%e A291968   0, 2,  6;
%e A291968   0, 2,  6;
%e A291968   0, 2, 12;
%e A291968   0, 2, 12, 24;
%e A291968   0, 2, 18, 24;
%e A291968   0, 2, 18, 48;
%e A291968   0, 2, 24, 72;
%e A291968   0, 2, 24, 96, 120.
%Y A291968 Row sums give A072576.
%Y A291968 Columns 0-1 give A000007, A007395.
%Y A291968 Cf. A216652.
%K A291968 nonn,tabf
%O A291968 0,3
%A A291968 _Seiichi Manyama_, Sep 07 2017