A355005 Table read by rows. T(n, k) = n*((k + n)!)^2/((k + n)*(n!)^2*k!) for n > 0 and T(0, 0) = 1.

1, 1, 2, 1, 6, 36, 1, 12, 120, 1200, 1, 20, 300, 4200, 58800, 1, 30, 630, 11760, 211680, 3810240, 1, 42, 1176, 28224, 635040, 13970880, 307359360, 1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480, 1, 72, 3240, 118800, 3920400, 122316480, 3710266560, 111307996800, 3339239904000

Offset

0,3

Links

Table of n, a(n) for n=0..44.

Formula

T(n, k) = Lah(k + n, n), where Lah denotes the unsigned Lah numbers A271703.

Example

[0] 1;
[1] 1,  2;
[2] 1,  6,   36;
[3] 1, 12,  120,  1200;
[4] 1, 20,  300,  4200,   58800;
[5] 1, 30,  630, 11760,  211680,  3810240;
[6] 1, 42, 1176, 28224,  635040, 13970880,  307359360;
[7] 1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480;

Maple

T := (n, k) -> ifelse(n = 0, 1, n*((k + n)!)^2 / ((k + n)*(n!)^2*k!)):
seq(seq(T(n, k), k = 0..n), n = 0..8);

Crossrefs

T(n, 1) = A002378, T(n, n) = A187535, A355004 (row sums), A271703 (Lah).

Sequence in context: A268371 A318918 A100404 * A320570 A300911 A347899

Adjacent sequences: A355002 A355003 A355004 * A355006 A355007 A355008

Keyword

nonn,tabl

Author

Peter Luschny, Jun 15 2022

Status

approved