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A176022
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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)!)
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0
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-2, 3, 3, -7, -18, -7, 25, 96, 96, 25, -121, -650, -800, -650, -121, 721, 5490, 7500, 7500, 5490, 721, -5041, -53067, -92610, -73500, -92610, -53067, -5041, 40321, 564704, 1328096, 987840, 987840, 1328096, 564704, 40321, -362881, -6532164
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OFFSET
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1,1
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COMMENTS
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Row sums are:
{-2, 6, -32, 242, -2342, 27422, -374936, 5841922, -101897354, 1962916022,...}.
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LINKS
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Table of n, a(n) for n=1..38.
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FORMULA
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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)!)
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EXAMPLE
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{-2},
{3, 3},
{-7, -18, -7},
{25, 96, 96, 25},
{-121, -650, -800, -650, -121},
{721, 5490, 7500, 7500, 5490, 721},
{-5041, -53067, -92610, -73500, -92610, -53067, -5041},
{40321, 564704, 1328096, 987840, 987840, 1328096, 564704, 40321},
{-362881, -6532164, -20345472, -18373824, -10668672, -18373824, -20345472, -6532164, -362881},
{3628801, 81648450, 326640600, 382838400, 186701760, 186701760, 382838400, 326640600, 81648450, 3628801}
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MATHEMATICA
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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)!);
Table[Table[L[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
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Cf. A008297
Sequence in context: A136122 A121875 A036251 * A316275 A113031 A127582
Adjacent sequences: A176019 A176020 A176021 * A176023 A176024 A176025
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KEYWORD
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sign,tabl,uned
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AUTHOR
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Roger L. Bagula, Apr 06 2010
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STATUS
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approved
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