A360335 Array read by antidiagonals downwards: A(n,m) = number of set partitions of [2n] into 2-element subsets {i, i+k} with 1 <= k <= m.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 7, 5, 1, 1, 3, 12, 16, 8, 1, 1, 3, 15, 35, 38, 13, 1, 1, 3, 15, 63, 105, 89, 21, 1, 1, 3, 15, 90, 226, 329, 209, 34, 1, 1, 3, 15, 105, 417, 841, 1014, 491, 55, 1, 1, 3, 15, 105, 645, 1787, 3251, 3116, 1153, 89, 1

Offset: 1

Author

Peter Dolland, Feb 03 2023

Keywords

• nonn
• tabl

Examples

			Square array begins:
  1,  1,    1,    1,     1,      1,      1,       1,       1, ...
  1,  2,    3,    3,     3,      3,      3,       3,       3, ...
  1,  3,    7,   12,    15,     15,     15,      15,      15, ...
  1,  5,   16,   35,    63,     90,    105,     105,     105, ...
  1,  8,   38,  105,   226,    417,    645,     840,     945, ...
  1, 13,   89,  329,   841,   1787,   3348,    5445,    7665, ...
  1, 21,  209, 1014,  3251,   7938,  16717,   31647,   53250, ...
  1, 34,  491, 3116, 12483,  36500,  86311,  180560,  344403, ...
  1, 55, 1153, 9610, 47481, 167631, 459803, 1062435, 2211181, ...
  ...
		

Crossrefs

Main diagonal is A014307.

Columns 1..4 are A000012, A000045(n+1), A052967, A320346.

Cf. A001147, A104443, A360333, A360334.

Formula

A(n,m) = A001147(n) = A104443(n,2) for m >= 2n - 1.