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A137499
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A triangular sequence of coefficients from a La Place Transform of a Bernoulli expansion function :LaplaceTransform[t*Exp[x*t]/(Exp[t] - 1), t, 1/t] =Zeta[2,1+1/t-x]->shifted to Zeta[6,1+1/t-x].
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0
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0, 0, 0, 0, 0, 24, -360, 720, 2520, -15120, 15120, 0, 141120, -423360, 282240, -169344, 0, 5080320, -10160640, 5080320, 0, -15240960, 0, 152409600, -228614400, 91445760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Row sums:
{0, 0, 0, 0, 0, 24, 360, 2520, 0, -169344, 0};
These functions are due the close connection of the Bernoulli type functions with the Zeta ( generalized) functions.
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FORMULA
| Zeta[6,1+1/t-x]=Sum[1/(n+1/t+x)^6,{n,0,Infinity}]=Sum[p(x,n)*t^n/n!,{n,0,Infinity}]; out(n,m)=n!*Coefficients(p(x,n)).
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EXAMPLE
| {0},
{0},
{0},
{0},
{0},
{24},
{-360,720},
{2520, -15120, 15120},
{0, 141120, -423360, 282240},
{-169344, 0, 5080320, -10160640, 5080320},
{0, -15240960, 0, 152409600, -228614400, 91445760}
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MATHEMATICA
| LaplaceTransform[t*Exp[x*t]/(Exp[t] - 1), t, s]; Clear[p, f, g] p[t_] = Zeta[6, 1 + 1/t - x]; Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ FullSimplify[Series[p[t], {t, 0, 30}]], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Sequence in context: A022748 A004325 A075621 * A122813 A028245 A005546
Adjacent sequences: A137496 A137497 A137498 * A137500 A137501 A137502
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KEYWORD
| uned,tabf,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 22 2008
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