A094456 - OEIS

%I #19 Mar 18 2023 16:49:34

%S 1,0,1,0,1,2,0,1,5,5,0,1,10,22,14,0,1,19,70,93,42,0,1,36,201,421,386,

%T 132,0,1,69,559,1657,2324,1586,429,0,1,134,1548,6162,11836,12136,6476,

%U 1430,0,1,263,4316,22445,55843,76928,60948,26333,4862,0,1,520,12163,81451,254415,444666,467426,297335,106762,16796

%N Triangle T(n,k), 0<=k<=n, read by rows; given by [0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938.

%C Diagonals : A000007, A000012, A052944; A000108, A000346.

%C Triangle :

%C   1;

%C   0, 1;

%C   0, 1,  2;

%C   0, 1,  5,  5;

%C   0, 1, 10, 22, 14;

%C   ...

%C The alternating sum is (-1)^n = A033999(n). - _F. Chapoton_, Mar 18 2023

%H Alois P. Heinz, <a href="/A094456/b094456.txt">Rows n = 0..150, flattened</a>

%F Sum_{k=0..n} T(n,k) = A090365(n).

%Y Cf. A000108 (main diagonal), A033999, A084938, A090365 (row sums).

%K nonn,tabl

%O 0,6

%A _Philippe Deléham_, Jun 04 2004