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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
-1, 2, 1, -6, -9, -1, 24, 72, 24, 1, -120, -600, -400, -50, -1, 720, 5400, 6000, 1500, 90, 1, -5040, -52920, -88200, -36750, -4410, -147, -1, 40320, 564480, 1317120, 823200, 164640, 10976, 224, 1, -362880, -6531840, -20321280, -17781120, -5334336 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are:

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

LINKS

Table of n, a(n) for n=1..41.

FORMULA

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

EXAMPLE

{-1},

{2, 1},

{-6, -9, -1},

{24, 72, 24, 1},

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

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

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

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

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

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

MATHEMATICA

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

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

Flatten[%]

CROSSREFS

Cf. A008297

Sequence in context: A021465 A139526 A248927 * A263255 A145663 A276664

Adjacent sequences:  A176010 A176011 A176012 * A176014 A176015 A176016

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 06 2010

STATUS

approved

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)