%I #20 Jun 11 2023 11:50:53

%S 1,2,2,2,3,4,2,10,4,12,4,2,22,8,4,26,20,3,34,40,4,44,60,8,2,54,100,16,

%T 6,58,148,40,2,74,208,80,4,88,268,160,4,88,388,240,16,5,110,468,416,

%U 32,2,118,616,616,80,6,136,736,936,160,2,142,940,1296,320,6,162,1108,1816,576

%N Irregular triangle read by rows in which T(n,k) is one half of the number of overpartitions of n having k distinct parts, n>=1, k>=1.

%F T(n,k) = (1/2)*A235790(n,k).

%F T(n,k) = (2^(k-1))*A116608(n,k).

%e Triangle begins:

%e 1;

%e 2;

%e 2, 2;

%e 3, 4;

%e 2, 10;

%e 4, 12, 4;

%e 2, 22, 8;

%e 4, 26, 20;

%e 3, 34, 40;

%e 4, 44, 60, 8;

%e 2, 54, 100, 16;

%e 6, 58, 148, 40;

%e 2, 74, 208, 80;

%e 4, 88, 268, 160;

%e 4, 88, 388, 240, 16;

%e ...

%Y Column 1 gives A000005.

%Y Row n has length A003056(n).

%Y Row sums give A014968, n >= 1.

%Y The first element of column k is A000079(k-1).

%Y The first element of column k is in row A000217(k).

%Y Cf. A116608, A235790.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Mar 31 2023