A291968 - OEIS

%I #20 Sep 07 2017 09:29:12

%S 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 0,2,24,96,120,0,2,30,120,120,0,2,30,168,240,0,2,36,192,360,0,2,36,

%U 240,600,0,2,42,288,720,720,0,2,42,336,1080,720,0,2,48,384

%N 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 Seiichi Manyama, <a href="/A291968/b291968.txt">Rows n = 0..481, flattened</a>

%F G.f. of column k: (k+1)! * x^(k*(k+1)/2) / Product_{j=1..k} (1-x^j).

%e First few rows are:

%e   1;

%e   0, 2;

%e   0, 2;

%e   0, 2,  6;

%e   0, 2,  6;

%e   0, 2, 12;

%e   0, 2, 12, 24;

%e   0, 2, 18, 24;

%e   0, 2, 18, 48;

%e   0, 2, 24, 72;

%e   0, 2, 24, 96, 120.

%Y Row sums give A072576.

%Y Columns 0-1 give A000007, A007395.

%Y Cf. A216652.

%K nonn,tabf

%O 0,3

%A _Seiichi Manyama_, Sep 07 2017