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A009999 Triangle in which j-th entry in i-th row is (i+1-j)^j, 0<=j<=i. 5
1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 8, 1, 1, 5, 16, 27, 16, 1, 1, 6, 25, 64, 81, 32, 1, 1, 7, 36, 125, 256, 243, 64, 1, 1, 8, 49, 216, 625, 1024, 729, 128, 1, 1, 9, 64, 343, 1296, 3125, 4096, 2187, 256, 1, 1, 10, 81, 512, 2401, 7776, 15625, 16384, 6561, 512, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 24.

LINKS

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

FORMULA

T(n,0) = 1; T(n,k) = (n-k+1)*T(n-1,k-1) for k=1..n. - Reinhard Zumkeller, Feb 02 2014

EXAMPLE

1

1 1

1 2 1

1 3 4 1

1 4 9 8 1

1 5 16 27 16 1

1 6 25 64 81 32 1

1 7 36 125 256 243 64 1

1 8 49 216 625 1024 729 128 1

1 9 64 343 1296 3125 4096 2187 256 1

1 10 81 512 2401 7776 15625 16384 6561 512 1

MAPLE

A009999 := proc(i, j) (i+1-j)^j ; end proc: # R. J. Mathar, Jan 16 2011

MATHEMATICA

Table[(i+1-j)^j, {i, 0, 10}, {j, 0, i}] // Flatten (* Jean-Fran├žois Alcover, Jan 14 2014 *)

PROG

(Haskell)

a009999 n k = (n + 1 - k) ^ k

a009999_row n = a009999_tabl !! n

a009999_tabl = [1] : map snd (iterate f ([1, 1], [1, 1])) where

   f (us@(u:_), vs) = (us', 1 : zipWith (*) us' vs)

                      where us' = (u + 1) : us

-- Reinhard Zumkeller, Feb 02 2014

CROSSREFS

Cf. A095884, A051128.

Cf. A009998 (mirrored).

Sequence in context: A080853 A071922 A138028 * A322268 A144823 A098446

Adjacent sequences:  A009996 A009997 A009998 * A010000 A010001 A010002

KEYWORD

tabl,nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

T(10,8) corrected by Reinhard Zumkeller, Feb 02 2014

STATUS

approved

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Last modified May 19 23:16 EDT 2019. Contains 323411 sequences. (Running on oeis4.)