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 A176647 A symmetrical triangle sequence:t(n,m)=Binomial[n*(3*n - 1)/2 + m, m] + Binomial[n*(3*n - 1)/2 + n - m, n - m] - Binomial[n + n*(3*n - 1)/2, n] 0
 1, 1, 1, 1, -9, 1, 1, -351, -351, 1, 1, -12627, -14398, -12627, 1, 1, -575721, -648906, -648906, -575721, 1, 1, -32468384, -35945819, -36238644, -35945819, -32468384, 1, 1, -2186189329, -2387546394, -2403595518, -2403595518, -2387546394 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The sequence uses pentagonal numbers as the connectedness function. Row sums are: {1, 2, -7, -700, -39650, -2449252, -173067048, -13954662480, -1270600138500, -129219696586750, -14534235944709635,...}. LINKS FORMULA t(n,m)=Binomial[n*(3*n - 1)/2 + m, m] + Binomial[n*(3*n - 1)/2 + n - m, n - m] - Binomial[n + n*(3*n - 1)/2, n] EXAMPLE {1}, {1, 1}, {1, -9, 1}, {1, -351, -351, 1}, {1, -12627, -14398, -12627, 1}, {1, -575721, -648906, -648906, -575721, 1}, {1, -32468384, -35945819, -36238644, -35945819, -32468384, 1}, {1, -2186189329, -2387546394, -2403595518, -2403595518, -2387546394, -2186189329, 1}, {1, -171200862663, -185035271537, -186023309861, -186081250380, -186023309861, -185035271537, -171200862663, 1}, {1, -15290266473507, -16391165652705, -16462191132828, -16466225034336, -16466225034336, -16462191132828, -16391165652705, -15290266473507, 1}, {1, -1534076755992789, -1633692129747979, -1639551857097889, -1639860244637209, -1639873969757905, -1639860244637209, -1639551857097889, -1633692129747979, -1534076755992789, 1} MATHEMATICA t[n_, m_] = Binomial[n*( 3*n - 1)/2 + m, m] + Binomial[n*(3*n - 1)/2 + n - m, n - m] - Binomial[n + n*(3*n - 1)/2, n]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Cf. A000326, A176567 Sequence in context: A022172 A173005 A015123 * A068452 A021527 A257437 Adjacent sequences:  A176644 A176645 A176646 * A176648 A176649 A176650 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 22 2010 STATUS approved

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Last modified April 19 10:30 EDT 2021. Contains 343112 sequences. (Running on oeis4.)