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

1,5

Comments

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

Links

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Jean-Christophe Aval, François Bergeron, Interlaced rectangular parking functions, arXiv:1503.03991 [math.CO], 2015.

Formula

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

Example

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   |...

Crossrefs

Cf. A071201.

Sequence in context: A125127 A051120 A114476 * A117184 A035690 A124794

Adjacent sequences: A260416 A260417 A260418 * A260420 A260421 A260422

Keyword

nonn,tabl

Author

Michel Marcus, Jul 25 2015

Extensions

More terms from Alois P. Heinz, Nov 30 2015

Status

approved