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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
 -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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are: {-2, 6, -32, 242, -2342, 27422, -374936, 5841922, -101897354, 1962916022,...}. LINKS FORMULA 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)!) EXAMPLE {-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} MATHEMATICA 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[%] CROSSREFS Cf. A008297 Sequence in context: A136122 A121875 A036251 * A316275 A113031 A127582 Adjacent sequences:  A176019 A176020 A176021 * A176023 A176024 A176025 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 06 2010 STATUS approved

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Last modified January 28 06:00 EST 2021. Contains 340490 sequences. (Running on oeis4.)