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A176022 A symmetrical triangle sequence:t(n,m)= ((-1)^n* Binomial[ -1 + n, -1 + m] Binomial[ n, -1 + m] n!/(m*m!)) + ((-1)^n* Binomial[ -1 + n, -m + n] Binomial[n, -m + n] n!)/((1 - m + n) ( 1 - m + n)!) 0

%I

%S -2,3,3,-7,-18,-7,25,96,96,25,-121,-650,-800,-650,-121,721,5490,7500,

%T 7500,5490,721,-5041,-53067,-92610,-73500,-92610,-53067,-5041,40321,

%U 564704,1328096,987840,987840,1328096,564704,40321,-362881,-6532164

%N A symmetrical triangle sequence:t(n,m)= ((-1)^n* Binomial[ -1 + n, -1 + m] Binomial[ n, -1 + m] n!/(m*m!)) + ((-1)^n* Binomial[ -1 + n, -m + n] Binomial[n, -m + n] n!)/((1 - m + n) ( 1 - m + n)!)

%C Row sums are:

%C {-2, 6, -32, 242, -2342, 27422, -374936, 5841922, -101897354, 1962916022,...}.

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

%e {-2},

%e {3, 3},

%e {-7, -18, -7},

%e {25, 96, 96, 25},

%e {-121, -650, -800, -650, -121},

%e {721, 5490, 7500, 7500, 5490, 721},

%e {-5041, -53067, -92610, -73500, -92610, -53067, -5041},

%e {40321, 564704, 1328096, 987840, 987840, 1328096, 564704, 40321},

%e {-362881, -6532164, -20345472, -18373824, -10668672, -18373824, -20345472, -6532164, -362881},

%e {3628801, 81648450, 326640600, 382838400, 186701760, 186701760, 382838400, 326640600, 81648450, 3628801}

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

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

%t Flatten[%]

%Y Cf. A008297

%K sign,tabl,uned

%O 1,1

%A _Roger L. Bagula_, Apr 06 2010

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Last modified July 23 00:43 EDT 2019. Contains 325228 sequences. (Running on oeis4.)