A235999 Triangle read by rows: T(n,k) = 2^k*A235998(n,k), n>=1, k>=1.

2, 4, 4, 8, 6, 20, 4, 56, 8, 88, 48, 4, 176, 144, 8, 272, 448, 6, 428, 1168, 8, 688, 2496, 384, 4, 1044, 5416, 1344, 12, 1584, 10864, 4608, 4, 2424, 21328, 13152, 8, 3800, 40096, 35616, 8, 5656, 76336, 84864, 3840, 10, 8952, 140248, 200224, 15360

Offset: 1

Author

Omar E. Pol, Jan 19 2014

Keywords

• nonn
• tabf
• look

Comments

T(n,k) is also the number of overcompositions of n having k distinct parts. For the definition of overcomposition see A236002.

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

Row sums give A236002, n >= 1.

Column 1 is A062011.

T(k*(k+1)/2,k) = T(A000217(k),k) = A000165(k) = (2*k)!!. - Alois P. Heinz, Jan 20 2014

Examples

			Triangle begins:
2;
4;
4,     8;
6,    20;
4,    56;
8,    88,     48;
4,   176,    144;
8,   272,    448;
6,   428,   1168;
8,   688,   2496,    384;
4,  1044,   5416,   1344;
12, 1584,  10864,   4608;
4,  2424,  21328,  13152;
8,  3800,  40096,  35616;
8,  5656,  76336,  84864,  3840;
10, 8952, 140248, 200224, 15360;
...
		

Links

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

Crossrefs

Cf. A003056, A011782, A062011, A116608, A235790, A235998, A236002.

Extensions

More terms from Alois P. Heinz, Jan 20 2014