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Search: id:A137498
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| A137498 |
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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[5,1+1/t-x]. |
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+0
1
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| 0, 0, 0, 0, 6, -60, 120, 300, -1800, 1800, 0, 12600, -37800, 25200, -11760, 0, 352800, -705600, 352800, 0, -846720, 0, 8467200, -12700800, 5080320, 1814400, 0, -38102400, 0, 190512000, -228614400, 76204800
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums:
{0, 0, 0, 0, 6, 60, 300, 0, -11760, 0, 1814400};
These functions are due the close connection of the Bernoulli type functions with the Zeta ( generalized) functions.
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FORMULA
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Zeta[5,1+1/t-x]=Sum[1/(n+1/t+x)^5,{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
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{0},
{0},
{0},
{0},
{6},
{-60, 120},
{300, -1800, 1800},
{0, 12600, -37800, 25200},
{-11760, 0, 352800, -705600, 352800},
{0, -846720, 0, 8467200, -12700800, 5080320},
{1814400, 0, -38102400, 0, 190512000, -228614400, 76204800}
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MATHEMATICA
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LaplaceTransform[t*Exp[x*t]/(Exp[t] - 1), t, s]; Clear[p, f, g] p[t_] = Zeta[5, 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
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Sequence in context: A007358 A007357 A002827 this_sequence A036283 A126576 A121287
Adjacent sequences: A137495 A137496 A137497 this_sequence A137499 A137500 A137501
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KEYWORD
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nonn,uned,tabf
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 22 2008
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