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A123964 A triangular sequence from the omega(5) Jacobian Elliptic Modular equation. 0

%I

%S 0,-1,0,-64,-3,4080,-729,-128,29515,236160,-4096,-1215,123168,986873,

%T 4194240,-15625,-6144,373899,3004544,12770391,39062400,-46656,-21875,

%U 925648,7468533,31750240,97119349,241864560,-117649,-62208,1989555,16131200,68598447,209838336,522579107,1129900800

%N A triangular sequence from the omega(5) Jacobian Elliptic Modular equation.

%C Normally these functions are taken as implicit polynomials in two variables set equal to zero. Row sum: Table[Sum[t[n, m], {n, 0, m}], {m, 0, 10}] {0, -1, 4013, 264818, 5298970, 55189465, 379059799, 1948857588, 8093819508, 28530904515, 88314392705}

%D Eric Weisstein's World of Mathematics, "Modular Equation." http://mathworld.wolfram.com/ModularEquation.html

%F t(n,m) =n^6 - m^6 + 5*n^2*m^2*(n^2 - m^2) + 4*n*m*(n^4*m^4 - 1)

%e Triangular sequence:

%e {0},

%e {-1, 0},

%e {-64, -3, 4080},

%e {-729, -128, 29515, 236160},

%e {-4096, -1215,123168, 986873, 4194240},

%e {-15625, -6144, 373899, 3004544, 12770391, 39062400},

%e {-46656, -21875, 925648, 7468533, 31750240, 97119349, 241864560}

%t t[n_, m_] = n^6 - m^6 + 5*n^2*m^2*(n^2 - m^2) + 4*n*m*(n^4*m^4 - 1); a = Table[Table[t[n, m], {n, 0, m}], {m, 0, 10}]; Flatten[a]

%K uned,sign

%O 1,4

%A _Roger L. Bagula_, Oct 28 2006

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Last modified October 23 01:49 EDT 2020. Contains 337962 sequences. (Running on oeis4.)