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 A176021 A symmetrical triangle sequence:t(n,m)=1 - (-1)^n - (-1)^ n* n! + ((-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
 1, 1, 1, 1, -10, 1, 1, 72, 72, 1, 1, -528, -678, -528, 1, 1, 4770, 6780, 6780, 4770, 1, 1, -48025, -87568, -68458, -87568, -48025, 1, 1, 524384, 1287776, 947520, 947520, 1287776, 524384, 1, 1, -6169282, -19982590, -18010942, -10305790, -18010942 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: {1, 2, -8, 146, -1732, 23102, -339642, 5519362, -98631416, 1926628022,...}. LINKS FORMULA t(n,m)=1 - (-1)^n - (-1)^ n* n! + ((-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 {1}, {1, 1}, {1, -10, 1}, {1, 72, 72, 1}, {1, -528, -678, -528, 1}, {1, 4770, 6780, 6780, 4770, 1}, {1, -48025, -87568, -68458, -87568, -48025, 1}, {1, 524384, 1287776, 947520, 947520, 1287776, 524384, 1}, {1, -6169282, -19982590, -18010942, -10305790, -18010942, -19982590, -6169282, 1}, {1, 78019650, 323011800, 379209600, 183072960, 183072960, 379209600, 323011800, 78019650, 1} MATHEMATICA L[n_, m_] = 1 - (-1)^n - (-1)^ n* n! + ((-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: A142459 A157641 A129274 * A166972 A160562 A176243 Adjacent sequences:  A176018 A176019 A176020 * A176022 A176023 A176024 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 06 2010 STATUS approved

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