A162995 A scaled version of triangle A162990.

1, 3, 1, 12, 4, 1, 60, 20, 5, 1, 360, 120, 30, 6, 1, 2520, 840, 210, 42, 7, 1, 20160, 6720, 1680, 336, 56, 8, 1, 181440, 60480, 15120, 3024, 504, 72, 9, 1, 1814400, 604800, 151200, 30240, 5040, 720, 90, 10, 1

Offset: 1

Author

Johannes W. Meijer, Jul 27 2009

Keywords

• easy
• nonn
• tabl

Comments

We get this scaled version of triangle A162990 by dividing the coefficients in the left hand columns by their 'top-values' and then taking the square root.

T(n,k) = A173333(n+1,k+1), 1 <= k <= n. - Reinhard Zumkeller, Feb 19 2010

T(n,k) = A094587(n+1,k+1), 1 <= k <= n. - Reinhard Zumkeller, Jul 05 2012

Examples

			The first few rows of the triangle are:
[1]
[3, 1]
[12, 4, 1]
[60, 20, 5, 1]
		

Links

• Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened

Crossrefs

Cf. A094587.

A056542(n) equals the row sums for n>=1.

A001710, A001715, A001720, A001725, A001730, A049388, A049389, A049398, A051431 are related to the left hand columns.

A000012, A009056, A002378, A007531, A052762, A052787, A053625 and A159083 are related to the right hand columns.

Programs

Haskell

a162995 n k = a162995_tabl !! (n-1) !! (k-1)
a162995_row n = a162995_tabl !! (n-1)
a162995_tabl = map fst $ iterate f ([1], 3)
   where f (row, i) = (map (* i) row ++ [1], i + 1)
-- Reinhard Zumkeller, Jul 04 2012

Maple

a := proc(n, m): (n+1)!/(m+1)! end: seq(seq(a(n, m), m=1..n), n=1..9); # Johannes W. Meijer, revised Nov 23 2012

Mathematica

Table[(n+1)!/(m+1)!, {n, 10}, {m, n}] (* Paolo Xausa, Mar 31 2024 *)

Formula

a(n,m) = (n+1)!/(m+1)! for n = 1, 2, 3, ..., and m = 1, 2, ..., n.