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Search: id:A137481
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| A137481 |
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Triangular sequence based on the coefficients of the magnetic model for q=1/2: p(x,t)=Exp[x*t]*((t^2 + 1/2 - 1)/(2*t + 1/2 - 2))^2. |
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+0
1
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| 1, 8, 3, 24, 48, 9, -192, 216, 216, 27, -2976, -2304, 1296, 864, 81, -57600, -44640, -17280, 6480, 3240, 243, -1336320, -1036800, -401760, -103680, 29160, 11664, 729, -36126720, -28062720, -10886400, -2812320, -544320, 122472, 40824, 2187, -1114767360, -867041280, -336752640, -87091200
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are: {1, 11, 81, 267, -3039, -109557, -2837007, -78266997, -2424502719, -84168178677, -3241001149551};
These magnetic models are important in the application of nonlinear complex dynamics to physical systems.
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REFERENCES
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Peitgen and Richter, eds., The Beauty of Fractals, Springer-Verlag, New York, 1986, page145.
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FORMULA
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p(x,t)=Exp[x*t]*((t^2 + 1/2 - 1)/ (2*t + 1/2-2))^2=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=3^(n + 2)*n!*Coefficient(P(x,n))
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EXAMPLE
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{{1},
{8, 3},
{24, 48, 9},
{-192, 216, 216, 27},
{-2976, -2304, 1296, 864, 81},
{-57600, -44640, -17280, 6480, 3240, 243},
{-1336320, -1036800, -401760, -103680, 29160, 11664,729},
{-36126720, -28062720, -10886400, -2812320, -544320, 122472, 40824, 2187}, {-1114767360, -867041280, -336752640, -87091200, -16873920, -2612736, 489888, 139968, 6561},
{-38645268480, -30098718720, -11705057280, -3030773760, -587865600, -91119168,-11757312, 1889568, 472392, 19683},
{-1486356480000, -1159358054400, -451480780800, -117050572800, -22730803200, -3527193600, -455595840, -50388480, 7085880, 1574640, 59049}
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MATHEMATICA
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p[t_] =Exp[x*t]*((t^2 + 1/2 - 1)/(2*t + 1/2 - 2))^2; Table[ ExpandAll[3^(n + 2)*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[3^(n + 2)*n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A137478 A137479 A137480 this_sequence A137482 A137483 A137484
Sequence in context: A070486 A037206 A065530 this_sequence A004734 A049074 A038281
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KEYWORD
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tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008
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