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Search: id:A138106
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| A138106 |
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A triangular sequence of coefficients based on the expansion of a Morse potential type function: p(x,t)=Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t]). |
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+0
1
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| -1, 0, -1, 2, 0, -1, -6, 6, 0, -1, 14, -24, 12, 0, -1, -30, 70, -60, 20, 0, -1, 62, -180, 210, -120, 30, 0, -1, -126, 434, -630, 490, -210, 42, 0, -1, 254, -1008, 1736, -1680, 980, -336, 56, 0, -1, -510, 2286, -4536, 5208, -3780, 1764, -504, 72, 0, -1, 1022, -5100, 11430, -15120, 13020, -7560, 2940, -720, 90, 0, -1
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums are:
{-1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1};
The Morse potential is identified with simple
intermolecular energy to distance relationships.
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REFERENCES
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A. Messiah, Quantum mechanics, vol. 2, p. 795, fig.XVIII.2, North Holland, 1969.
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FORMULA
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p(x,t)=Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t])=sum(P(x,n)*t^n/n!,{n,0,Infinity}); Out_n,m=Coefficients(P(x,n)).
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EXAMPLE
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{-1},
{0, -1},
{2, 0, -1},
{-6, 6, 0, -1},
{14, -24, 12, 0, -1},
{-30, 70, -60, 20, 0, -1},
{62, -180, 210, -120, 30, 0, -1},
{-126, 434, -630, 490, -210, 42, 0, -1},
{254, -1008, 1736, -1680,980, -336, 56, 0, -1},
{-510, 2286, -4536, 5208, -3780, 1764, -504, 72, 0, -1},
{1022, -5100, 11430, -15120, 13020, -7560, 2940, -720, 90, 0, -1}
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MATHEMATICA
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p[t_] = Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t]); Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[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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Sequence in context: A114709 A089949 A085845 this_sequence A131689 A114329 A101371
Adjacent sequences: A138103 A138104 A138105 this_sequence A138107 A138108 A138109
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 03 2008
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