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Search: id:A137378
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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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+0
1
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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; listen)
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OFFSET
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1,8
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COMMENT
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Row sums are: {1, -1, 1, 5, -23, -181, 1681, 17849, -259055, -3446857, 69082561}
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REFERENCES
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Weisstein, Eric W. "Mott Polynomial." http://mathworld.wolfram.com/MottPolynomial.html
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FORMULA
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p(x) = Exp[x*(1 - Sqrt[1 + t^2])/t]; weights 2^n*n!;
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EXAMPLE
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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}
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MATHEMATICA
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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
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Adjacent sequences: A137375 A137376 A137377 this_sequence A137379 A137380 A137381
Sequence in context: A019185 A101109 A060297 this_sequence A084680 A051626 A137785
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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), Apr 09 2008
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