A235790 Triangle read by rows: T(n,k) = 2^k*A116608(n,k), n>=1, k>=1.

2, 4, 4, 4, 6, 8, 4, 20, 8, 24, 8, 4, 44, 16, 8, 52, 40, 6, 68, 80, 8, 88, 120, 16, 4, 108, 200, 32, 12, 116, 296, 80, 4, 148, 416, 160, 8, 176, 536, 320, 8, 176, 776, 480, 32, 10, 220, 936, 832, 64, 4, 236, 1232, 1232, 160, 12, 272, 1472, 1872, 320

Offset: 1

Author

Omar E. Pol, Jan 18 2014

Keywords

• nonn
• tabf
• look

Comments

It appears that T(n,k) is the number of overpartitions of n having k distinct parts. (This is true by definition, Joerg Arndt, Jan 20 2014).

Row n has length A003056(n) hence the first element of column k is in row A000217(k).

The first element of column k is A000079(k).

Examples

			Triangle begins:
2;
4;
4,    4;
6,    8;
4,   20;
8,   24,    8;
4,   44,   16;
8,   52,   40;
6,   68,   80;
8,   88,  120,   16;
4,  108,  200,   32;
12, 116,  296,   80;
4,  148,  416,  160;
8,  176,  536,  320;
8,  176,  776,  480,   32;
10, 220,  936,  832,   64;
4,  236, 1232, 1232,  160;
12, 272, 1472, 1872,  320;
4,  284, 1880, 2592,  640;
12, 324, 2216, 3632, 1152;
8,  328, 2704, 4944, 1856, 64;
...
		

Links

• Alois P. Heinz, Rows n = 1..500, flattened

Crossrefs

Row sums give A015128, n >= 1.

Column 1 is A062011.

Cf. A000217, A003056, A116608, A196020, A211971, A235792, A235793, A235797, A235798, A235999, A236000, A236001.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      expand(b(n, i-1)+add(x*b(n-i*j, i-1), j=1..n/i))))
    end:
T:= n->(p->seq(2^i*coeff(p, x, i), i=1..degree(p)))(b(n$2)):
seq(T(n), n=1..20);  # Alois P. Heinz, Jan 20 2014

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Expand[b[n, i-1] + Sum[x*b[n-i*j, i-1], {j, 1, n/i}]]]]; T[n_] := Function[p, Table[2^i * Coefficient[p, x, i], {i, 1, Exponent[p, x]}]][b[n, n]]; Table[T[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Oct 20 2016, after Alois P. Heinz *)