A260419 Square array T(n,m) read by antidiagonals, T(n,m) is the number of (m,n)-parking functions.

1, 1, 1, 1, 3, 1, 1, 3, 4, 1, 1, 5, 16, 11, 1, 1, 5, 16, 27, 16, 1, 1, 7, 25, 125, 81, 42, 1, 1, 7, 49, 125, 256, 378, 64, 1, 1, 9, 49, 243, 1296, 1184, 729, 163, 1, 1, 9, 64, 343, 1296, 3125, 4096, 2187, 256, 1, 1, 11, 100, 729, 2401, 16807, 15625, 27213, 9529, 638, 1

Offset: 1

Author

Michel Marcus, Jul 25 2015

Keywords

• nonn
• tabl

Comments

T(n,2) appears to be A027306(n).

Examples

			Table starts (see Table 1 in Aval & Bergeron link):
n/m  1   2    3    4     5
------------------------------
1   |1,  1,   1,   1,    1, ...
2   |1,  3,   3,   5,    5, ...
3   |1,  4,  16,  16,   25, ...
4   |1, 11,  27, 125,  125, ...
5   |1, 16,  81, 256, 1296, ...
6   |...
		

Links

• Alois P. Heinz, Antidiagonals n = 1..141, flattened
• Jean-Christophe Aval, François Bergeron, Interlaced rectangular parking functions, arXiv:1503.03991 [math.CO], 2015.

Crossrefs

Cf. A071201.

Formula

T(n,m) = m^(n-1), if m and n are coprime (see Lemma in Aval & Bergeron link).

Extensions

More terms from Alois P. Heinz, Nov 30 2015