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Search: id:A136426
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| A136426 |
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Triangular sequence from expansion of the harmonic number like polynomial : g(x,t)=x*Log[1 - t]/(1 - t)^x ( from (1-t)->(1-t)^x in Log[1 - t]/(1 - t) ). |
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+0
1
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| 0, 0, -1, 0, -1, -2, 0, -2, -6, -3, 0, -6, -22, -18, -4, 0, -24, -100, -105, -40, -5, 0, -120, -548, -675, -340, -75, -6, 0, -720, -3528, -4872, -2940, -875, -126, -7, 0, -5040, -26136, -39396, -27076, -9800, -1932, -196, -8, 0, -40320, -219168, -354372, -269136, -112245, -27216, -3822, -288, -9, 0, -362880
(list; table; graph; listen)
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OFFSET
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1,6
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COMMENT
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Row sums:
{0, -1, -3, -11, -50, -274, -1764, -13068, -109584, -1026576, -10628640}
You may get rid of the first column zeros by divining by x:
a = Table[n!* CoefficientList[Simplify[SeriesCoefficient[Series[p[t], {t, 0, 30}], n]/x], x], {n, 0, 10}];
Flatten[a]
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REFERENCES
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Sondow, Jonathan and Weisstein, Eric W., Harmonic Number, http://mathworld.wolfram.com/HarmonicNumber.html
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FORMULA
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g(x,t)=x*Log[1 - t]/(1 - t)^x=Sun[p(x,n)*t^n.n!,{n,1,Infinity}]; out_n,m=Coefficient(n!p(x,n)).
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EXAMPLE
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{0},
{0, -1},
{0, -1, -2},
{0, -2, -6, -3},
{0, -6, -22, -18, -4},
{0, -24, -100, -105, -40, -5},
{0, -120, -548, -675, -340, -75, -6},
{0, -720, -3528, -4872, -2940, -875, -126, -7},
{0, -5040, -26136, -39396, -27076, -9800, -1932, -196, -8},
{0, -40320, -219168, -354372, -269136, -112245, -27216, -3822, -288, -9},
{0, -362880, -2053152, -3518100, -2894720, -1346625, -379638, -66150, -6960,-405, -10}
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MATHEMATICA
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Clear[p, g] p[t_] = x*Log[1 - t]/(1 - t)^x; g = Table[ ExpandAll[n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[Simplify[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: A136423 A136424 A136425 this_sequence A136427 A136428 A136429
Sequence in context: A139213 A033727 A033757 this_sequence A094385 A057980 A081081
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KEYWORD
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tabl,uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 13 2008
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