A061314 Table read by descending antidiagonals where T(n,k) = T(n,k-1) + T(n,k-1)^2/k^2 and T(n,0)=n.

0, 0, 1, 0, 2, 2, 0, 3, 6, 3, 0, 4, 15, 12, 4, 0, 5, 40, 48, 20, 5, 0, 6, 140, 304, 120, 30, 6, 0, 7, 924, 6080, 1720, 255, 42, 7, 0, 8, 24640, 1484736, 186620, 7480, 483, 56, 8, 0, 9, 12415040, 61235956672, 1393267596, 3504380, 26404, 840, 72, 9, 0, 10

Offset: 0

Author

Henry Bottomley, Apr 24 2001

Keywords

• nonn
• tabl

Comments

Not always an integer.

Examples

			The table begins:
    0,       0,       0,       0,          0,...
    1,       2,       3,       4,          5,...
    2,       6,      15,      40,        140,...
    3,      12,      48,     304,       6080,...
    4,      20,     120,    1720,     186620,...
    5,      30,     255,    7480,    3504380,...
    6,      42,     483,   26404,   43599605,...
    7,      56,     840,   79240,  392515340,...
    8,      72,    1368,  209304, 2738219580,...
    ...
		

Crossrefs

Rows include A000004, A000027 and A061322. Columns include A001477, A002378, A061316, A061318 and A061320.

Formula

T(n, k) = T(n, k-1) + A061315(n, k)^2.