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URL: https://oeis.org/A138106

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A138106
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)).
2
-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
OFFSET
1,4
COMMENTS
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.
REFERENCES
A. Messiah, Quantum mechanics, vol. 2, p. 795, fig.XVIII.2, North Holland, 1969.
FORMULA
p(x,t) = exp(x*t)*(exp(-2*t) - 2*exp(-t)) = Sum_{n>=0} P(x,n)*t^n/n!.
EXAMPLE
Triangle begins as:
-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;
.....
MATHEMATICA
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}];
Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]//Flatten
CROSSREFS
Sequence in context: A264550 A089949 A085845 * A131689 A278075 A114329
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, May 03 2008
EXTENSIONS
Edited by G. C. Greubel, Apr 01 2019
STATUS
approved