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Search: id:A137393
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| A137393 |
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Triangular sequence from a Peters polynomials expansion: l0 = 2; m0 = 2; p(t) = (1 + t)^x/(1 + (1 + t)^l0)^m0. |
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+0
1
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| 1, -4, 2, 16, -20, 4, -48, 160, -72, 8, -96, -1120, 944, -224, 16, 3840, 6208, -10880, 4320, -640, 32, -46080, -12672, 115456, -72000, 16960, -1728, 64, 322560, -294912, -1146880, 1121792, -380800, 60032, -4480, 128, 645120, 4663296, 11223040, -17110016, 7933184, -1734656, 197120, -11264, 256
(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, -2, 0, 48, -480, 2880, 0, -322560, 5806080, -58060800, 0}
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REFERENCES
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Weisstein, Eric W. "Peters Polynomial." http://mathworld.wolfram.com/PetersPolynomial.html
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FORMULA
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l0 = 2; m0 = 2; p(t) = (1 + t)^x/(1 + (1 + t)^l0)^m0=Sum(s(x,k,l0,m0)*t^k/k!,{k,0,Infinity}]; Out(n,m)=2^(n+2)*n!*Coefficient(s(x,n,2,2))
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EXAMPLE
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{1},
{-4, 2},
{16, -20, 4},
{-48, 160, -72, 8},
{-96, -1120, 944, -224, 16},
{3840, 6208, -10880, 4320, -640, 32},
{-46080, -12672, 115456, -72000, 16960, -1728, 64},
{322560, -294912, -1146880, 1121792, -380800, 60032, -4480, 128},
{645120, 4663296, 11223040, -17110016, 7933184, -1734656, 197120, -11264, 256},
{-69672960, -1363968, -133447680, 268337152, -161344512, 45943296, -7096320, 611328, -27648, 512}, {1393459200, -1720442880, 2586968064, -4625121280, 3334430720, -1175516160, 231232512, -26757120, 1812480, -66560, 1024}
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MATHEMATICA
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Clear[p, l0, m0] l0 = 2; m0 = 2; p[t_] = (1 + t)^x/(1 + (1 + t)^l0)^m0 Table[ ExpandAll[2^(n + 2)*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[2^(n + 2)*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: A137390 A137391 A137392 this_sequence A137394 A137395 A137396
Sequence in context: A053125 A038232 A084623 this_sequence A122749 A074676 A117692
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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 10 2008
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