A089759 - OEIS

A089759

Table T(n,k), 0<=k, 0<=n, read by antidiagonals, defined by T(n,k) = (k*n)! / (n!)^k.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 6, 1, 1, 1, 24, 90, 20, 1, 1, 1, 120, 2520, 1680, 70, 1, 1, 1, 720, 113400, 369600, 34650, 252, 1, 1, 1, 5040, 7484400, 168168000, 63063000, 756756, 924, 1, 1, 1, 40320, 681080400, 137225088000, 305540235000, 11732745024, 17153136, 3432, 1, 1

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OFFSET

0,8

COMMENTS

T(n,k) is the number of lattice paths from {n}^k to {0}^k using steps that decrement one component by 1. - Alois P. Heinz, May 06 2013

LINKS

Alois P. Heinz, Antidiagonals n = 0..32, flattened

T. Chappell, A. Lascoux, S. Ole Warnaar, W. Zudilin, Logarithmic and complex constant term identities, arXiv:1112.3130 [math.CO], 2012.

EXAMPLE

Row n=0: 1, 1, 1, 1, 1, 1, ... A000012

Row n=1: 1, 1, 2, 6, 24, 120, ... A000142

Row n=2: 1, 1, 6, 90, 2520, 113400, ... A000680

Row n=3: 1, 1, 20, 1680, 369600, 168168000, ... A014606

Row n=4: 1, 1, 70, 34650, 63063000, 305540235000, ... A014608

Row n=5: 1, 1, 252, 756756, 11732745024, 623360743125120, ... A014609

MAPLE

T:= (n, k)-> (k*n)!/(n!)^k:

seq(seq(T(n, d-n), n=0..d), d=0..10); # Alois P. Heinz, Aug 16 2012

MATHEMATICA

T[n_, k_] := (k*n)!/(n!)^k; Table[T[n-k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Dec 19 2015 *)

CROSSREFS

Cf. A000680, A014606, A014608, A014609, A000984, A187783 (transposed version).

Main diagonal gives A034841.

Cf. A210472, A225094.

Sequence in context: A227655 A064992 A187783 * A325970 A347781 A088152

Adjacent sequences: A089756 A089757 A089758 * A089760 A089761 A089762

KEYWORD

easy,tabl,nonn

AUTHOR

Philippe Deléham, Jan 08 2004; revised Jun 08 2005

EXTENSIONS

Corrected by Alois P. Heinz, Aug 16 2012

STATUS

approved