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Search: id:A137369
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| A137369 |
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A triangular sequence based on a coefficient expansion of a kind of Boole Polynomial( Lambda=n);b(x,n,Lambda)=b(x,n): Expansion of p(t) = (1 + t)^x/(1 + (1 + t)^n) with weight factor 2^(n+1)*n!. |
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+0
1
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| 1, -1, 2, 4, -12, 4, 30, 88, -60, 8, -1344, 224, 752, -224, 16, -16920, -31232, 0, 4320, -720, 32, 2977920, -430848, -371264, -10560, 19840, -2112, 64, 53267760, 104934912, -5789056, -3084928, -101920, 78848, -5824, 128, -24148131840, 1882583040, 1867684864, -54942720, -20344576, -645120, 283136
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are: {1, 1, -4, 66, -576, -44520,2183040, 149299920, -20473528320, -1617320960640, 470995131801600}
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REFERENCES
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Weisstein, Eric W. "Boole Polynomial." >http://mathworld.wolfram.com/BoolePolynomial.html
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FORMULA
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Expansion of p(t) = (1 + t)^x/(1 + (1 + t)^n) with weight factor 2^(n+1)*n!: out[x,n)=2^(n-1)*b(x,n)
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EXAMPLE
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{1},
{-1, 2},
{4, -12, 4},
{30, 88, -60, 8},
{-1344, 224, 752, -224, 16},
{-16920, -31232,0, 4320, -720, 32},
{2977920, -430848, -371264, -10560, 19840, -2112, 64},
{53267760, 104934912, -5789056, -3084928, -101920, 78848, -5824, 128},
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MATHEMATICA
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Clear[p] p[t_] = (1 + t)^x/(1 + (1 + t)^n) Table[ ExpandAll[2^(n + 1)*n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[2^(n + 1)*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: A137366 A137367 A137368 this_sequence A137370 A137371 A137372
Sequence in context: A057284 A070314 A075554 this_sequence A000348 A141668 A087796
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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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