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Search: id:A137381
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| A137381 |
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Triangular sequence of coefficients from expansion of Narumi polynomials: generated by:p(x) = (t/Log[1 + t])^a0*(1 + t)^x; a0=2;weights (n+1)!*n!;. |
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+0
1
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| 1, 2, 2, 1, 6, 6, 0, -12, 0, 24, -12, 120, 0, -240, 120, 360, -2280, 0, 4800, -3600, 720, -13260, 68040, 0, -151200, 138600, -45360, 5040, 638400, -2899680, 0, 6773760, -7056000, 2963520, -564480, 40320, -39630528, 166320000, 0, -406425600, 464002560, -228614400, 57576960, -7257600, 362880
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are: {1, 4, 13, 12, -12, 0, 1860, -104160, 6334272, -465212160, 41650459200}
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REFERENCES
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Weisstein, Eric W. "Narumi Polynomial." http://mathworld.wolfram.com/NarumiPolynomial.html
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FORMULA
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p(x) = (t/Log[1 + t])^a0*(1 + t)^x; a0=2;weights (n+1)!*n!;
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EXAMPLE
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{1},
{2, 2},
{1, 6, 6},
{0, -12, 0, 24},
{-12, 120, 0, -240, 120},
{360, -2280, 0, 4800, -3600, 720},
{-13260, 68040, 0, -151200, 138600, -45360, 5040},
{638400, -2899680, 0, 6773760, -7056000, 2963520, -564480, 40320}
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MATHEMATICA
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Clear[p, x, t, a0] a0 = 2; p[t_] = (t/Log[1 + t])^a0*(1 + t)^x; Table[ ExpandAll[(n!*(n + 1)!)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[(n!*(n + 1)!)*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: A137378 A137379 A137380 this_sequence A137382 A137383 A137384
Sequence in context: A127743 A125278 A134558 this_sequence A109316 A094587 A135878
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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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