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A174298 A symmetrical triangle: t(n,m)=Binomial[n, m]*If[Floor[n/2] greater than or equal to m, n!/m!, n!/(n - m)! ] 0
1, 1, 1, 2, 4, 2, 6, 18, 18, 6, 24, 96, 72, 96, 24, 120, 600, 600, 600, 600, 120, 720, 4320, 5400, 2400, 5400, 4320, 720, 5040, 35280, 52920, 29400, 29400, 52920, 35280, 5040, 40320, 322560, 564480, 376320, 117600, 376320, 564480, 322560, 40320, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are:

{1, 2, 8, 48, 312, 2640, 23280, 245280, 2724960, 34292160, 459406080,...}.

LINKS

Table of n, a(n) for n=0..45.

FORMULA

t(n,m)=Binomial[n, m]*If[Floor[n/2] greater than or equal to m, n!/m!, n!/(n - m)! ]

EXAMPLE

{1},

{1, 1},

{2, 4, 2},

{6, 18, 18, 6},

{24, 96, 72, 96, 24},

{120, 600, 600, 600, 600, 120},

{720, 4320, 5400, 2400, 5400, 4320, 720},

{5040, 35280, 52920, 29400, 29400, 52920, 35280, 5040},

{40320, 322560, 564480, 376320, 117600, 376320, 564480, 322560, 40320},

{362880, 3265920, 6531840, 5080320, 1905120, 1905120, 5080320, 6531840, 3265920, 362880},

{3628800, 36288000, 81648000, 72576000, 31752000, 7620480, 31752000, 72576000, 81648000, 36288000, 3628800}

MATHEMATICA

Table[Table[ Binomial[n, m]*If[Floor[n/2] >= m, n!/m!, n!/(n - m)! ], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A138024 A167656 A253666 * A196347 A021012 A229460

Adjacent sequences:  A174295 A174296 A174297 * A174299 A174300 A174301

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 15 2010

STATUS

approved

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Last modified April 23 12:15 EDT 2021. Contains 343204 sequences. (Running on oeis4.)