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A176013 Triangle read by rows:t(n,m)=(-1)^n*(n!/m!)*(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m) 0

%I

%S -1,2,1,-6,-9,-1,24,72,24,1,-120,-600,-400,-50,-1,720,5400,6000,1500,

%T 90,1,-5040,-52920,-88200,-36750,-4410,-147,-1,40320,564480,1317120,

%U 823200,164640,10976,224,1,-362880,-6531840,-20321280,-17781120,-5334336

%N Triangle read by rows:t(n,m)=(-1)^n*(n!/m!)*(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)

%C Row sums are:

%C {-1, 3, -16, 121, -1171, 13711, -187468, 2920961, -50948677, 981458011,...}.

%F t(n,m)=(-1)^n*(n!/m!)*(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)

%e {-1},

%e {2, 1},

%e {-6, -9, -1},

%e {24, 72, 24, 1},

%e {-120, -600, -400, -50, -1},

%e {720, 5400, 6000, 1500, 90, 1},

%e {-5040, -52920, -88200, -36750, -4410, -147, -1},

%e {40320, 564480, 1317120, 823200, 164640, 10976, 224, 1},

%e {-362880, -6531840, -20321280, -17781120, -5334336, -592704, -24192, -324, -1},

%e {3628800, 81648000, 326592000, 381024000, 160030080, 26671680, 1814400, 48600, 450, 1 }

%t L[n_, m_] = (-1)^n*(n!/m!)*(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m);

%t Table[Table[L[n, m], {m, 1, n}], {n, 1, 10}];

%t Flatten[%]

%Y Cf. A008297

%K sign,tabl,uned

%O 1,2

%A _Roger L. Bagula_, Apr 06 2010

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Last modified November 14 17:47 EST 2019. Contains 329126 sequences. (Running on oeis4.)