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A123964 A triangular sequence from the omega(5) Jacobian Elliptic Modular equation. 0
0, -1, 0, -64, -3, 4080, -729, -128, 29515, 236160, -4096, -1215, 123168, 986873, 4194240, -15625, -6144, 373899, 3004544, 12770391, 39062400, -46656, -21875, 925648, 7468533, 31750240, 97119349, 241864560, -117649, -62208, 1989555, 16131200, 68598447, 209838336, 522579107, 1129900800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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}

REFERENCES

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

LINKS

Table of n, a(n) for n=1..36.

FORMULA

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

EXAMPLE

Triangular sequence:

{0},

{-1, 0},

{-64, -3, 4080},

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

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

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

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

MATHEMATICA

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]

CROSSREFS

Sequence in context: A301911 A302155 A288923 * A298923 A210114 A236179

Adjacent sequences:  A123961 A123962 A123963 * A123965 A123966 A123967

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula, Oct 28 2006

STATUS

approved

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)