A369019 - OEIS

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A369019

Triangle read by rows: T(n, k) = binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k).

3

0, 0, 1, 0, 2, 4, 0, 9, 12, 36, 0, 64, 72, 144, 432, 0, 625, 640, 1080, 2160, 6400, 0, 7776, 7500, 11520, 19440, 38400, 112500, 0, 117649, 108864, 157500, 241920, 403200, 787500, 2286144, 0, 2097152, 1882384, 2612736, 3780000, 5734400, 9450000, 18289152, 52706752

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

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

FORMULA

T = A369018 - A368849.

EXAMPLE

Triangle starts:

[0] [0]

[1] [0, 1]

[2] [0, 2, 4]

[3] [0, 9, 12, 36]

[4] [0, 64, 72, 144, 432]

[5] [0, 625, 640, 1080, 2160, 6400]

[6] [0, 7776, 7500, 11520, 19440, 38400, 112500]

[7] [0, 117649, 108864, 157500, 241920, 403200, 787500, 2286144]

MAPLE

T := (n, k) -> binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k):

seq(seq(T(n, k), k = 0..n), n=0..9);

MATHEMATICA

A369019[n_, k_] := Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k);

Table[A369019[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jan 27 2024 *)

PROG

(SageMath)

def A369019(n, k):

return binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k)

CROSSREFS

Cf. A369018, A368849.

Sequence in context: A021419 A338168 A180192 * A066529 A052080 A261754

Adjacent sequences: A369016 A369017 A369018 * A369020 A369021 A369022

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Jan 13 2024

STATUS

approved