A291969 - OEIS

%I #17 Sep 07 2017 09:43:24

%S 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 30,60,24,0,1,62,96,24,0,1,62,198,72,0,1,126,270,144,0,1,126,474,336,

%U 0,1,254,780,480,120,0,1,254,1188,1080,120,0,1,510,1800

%N 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 Seiichi Manyama, <a href="/A291969/b291969.txt">Rows n = 0..481, flattened</a>

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

%e First few rows are:

%e   1;

%e   0, 1;

%e   0, 1;

%e   0, 1,  2;

%e   0, 1,  2;

%e   0, 1,  6;

%e   0, 1,  6,  6;

%e   0, 1, 14,  6;

%e   0, 1, 14, 18;

%e   0, 1, 30, 36;

%e   0, 1, 30, 60, 24.

%Y Row sums give A204858.

%Y Columns 0-1 give A000007, A000012.

%Y Cf. A291960.

%K nonn,tabf

%O 0,8

%A _Seiichi Manyama_, Sep 07 2017