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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 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.)