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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

%I

%S 1,1,1,1,-9,1,1,-351,-351,1,1,-12627,-14398,-12627,1,1,-575721,

%T -648906,-648906,-575721,1,1,-32468384,-35945819,-36238644,-35945819,

%U -32468384,1,1,-2186189329,-2387546394,-2403595518,-2403595518,-2387546394

%N 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]

%C The sequence uses pentagonal numbers as the connectedness function.

%C Row sums are:

%C {1, 2, -7, -700, -39650, -2449252, -173067048, -13954662480, -1270600138500,

%C -129219696586750, -14534235944709635,...}.

%F 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]

%e {1},

%e {1, 1},

%e {1, -9, 1},

%e {1, -351, -351, 1},

%e {1, -12627, -14398, -12627, 1},

%e {1, -575721, -648906, -648906, -575721, 1},

%e {1, -32468384, -35945819, -36238644, -35945819, -32468384, 1},

%e {1, -2186189329, -2387546394, -2403595518, -2403595518, -2387546394, -2186189329, 1},

%e {1, -171200862663, -185035271537, -186023309861, -186081250380, -186023309861, -185035271537, -171200862663, 1},

%e {1, -15290266473507, -16391165652705, -16462191132828, -16466225034336, -16466225034336, -16462191132828, -16391165652705, -15290266473507, 1},

%e {1, -1534076755992789, -1633692129747979, -1639551857097889, -1639860244637209, -1639873969757905, -1639860244637209, -1639551857097889, -1633692129747979, -1534076755992789, 1}

%t 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];

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%Y Cf. A000326, A176567

%K sign,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Apr 22 2010

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Last modified May 8 02:26 EDT 2021. Contains 343652 sequences. (Running on oeis4.)