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A162995 A scaled version of triangle A162990. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

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

FORMULA

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

EXAMPLE

The first few rows of the triangle are:

[1]

[3, 1]

[12, 4, 1]

[60, 20, 5, 1]

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

PROG

(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

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.

Sequence in context: A287462 A287985 A117375 * A177020 A226167 A185105

Adjacent sequences:  A162992 A162993 A162994 * A162996 A162997 A162998

KEYWORD

easy,nonn,tabl

AUTHOR

Johannes W. Meijer, Jul 27 2009

STATUS

approved

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)