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A137378
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Triangular sequence of coefficients from expansion of Mott polynomials: generated by p(x) = Exp[x*(1 - Sqrt[1 + t^2])/t]; weights 2^n*n!;.
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1, 0, -1, 0, 0, 1, 0, 6, 0, -1, 0, 0, -24, 0, 1, 0, -240, 0, 60, 0, -1, 0, 0, 1800, 0, -120, 0, 1, 0, 25200, 0, -7560, 0, 210, 0, -1, 0, 0, -282240, 0, 23520, 0, -336, 0, 1, 0, -5080320, 0, 1693440, 0, -60480, 0, 504, 0, -1, 0, 0, 76204800, 0, -7257600, 0, 136080, 0, -720, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| Row sums are: {1, -1, 1, 5, -23, -181, 1681, 17849, -259055, -3446857, 69082561}
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REFERENCES
| Weisstein, Eric W. "Mott Polynomial." http://mathworld.wolfram.com/MottPolynomial.html
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FORMULA
| p(x) = Exp[x*(1 - Sqrt[1 + t^2])/t]; weights 2^n*n!;
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EXAMPLE
| {1},
{0, -1},
{0, 0, 1},
{0, 6, 0, -1},
{0, 0, -24, 0, 1},
{0, -240,0, 60, 0, -1},
{0, 0, 1800, 0, -120, 0, 1},
{0, 25200, 0, -7560, 0, 210, 0, -1},
{0, 0, -282240, 0, 23520, 0, -336, 0, 1},
{0, -5080320, 0, 1693440, 0, -60480, 0, 504, 0, -1},
{0, 0, 76204800, 0, -7257600, 0, 136080, 0, -720, 0, 1}
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MATHEMATICA
| Clear[p, x, t] p[t_] = Exp[x*(1 - Sqrt[1 + t^2])/t]; Table[ ExpandAll[2^(n)*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[2^(n)*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Sequence in context: A101109 A192072 A060297 * A084680 A051626 A200229
Adjacent sequences: A137375 A137376 A137377 * A137379 A137380 A137381
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 09 2008
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