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 A142147 Irregular triangle read by rows: first row is 1, and the n-th row gives the coefficients in the expansion of (1/2*x)*(1 - 2*x*(1 - x))^(n + 1)*Li(-n, 2*x*(1 - x)), where Li(n, z) is the polylogarithm. 8
 1, 1, -1, 1, 1, -4, 2, 1, 7, -12, -4, 12, -4, 1, 21, 0, -102, 100, 4, -32, 8, 1, 51, 160, -532, -24, 904, -672, 48, 80, -16, 1, 113, 980, -1094, -5128, 8760, -736, -6224, 3920, -432, -192, 32, 1, 239, 4284, 5276, -43964, 19764, 90272, -114080, 19824, 36304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Eric Weisstein's World of Mathematics, Polylogarithm FORMULA E.g.f.: ((1 - x)*(1 - 2*x)*exp(t*(1 + 2*x^2)) + x*exp(2*t*x))/(exp(2*t*x) - 2*x*(1 - x)*exp(t*(1 + 2*x^2))). - Franck Maminirina Ramaharo, Oct 22 2018 EXAMPLE Triangle begins:      1;      1, -1;      1,  1,  -4,    2;      1,  7, -12,   -4,  12,  -4;      1, 21,   0, -102, 100,   4,  -32,  8;      1, 51, 160, -532, -24, 904, -672, 48, 80, -16;       ... reformatted. - Franck Maminirina Ramaharo, Oct 21 2018 MATHEMATICA p[x_, n_] = If[n == 0, 1, (1 + 2*(-1 + x)*x)^(n + 1)*PolyLog[-n, 2*x*(1 - x)]/(2*x)]; Table[CoefficientList[FullSimplify[Expand[p[x, n]]], x], {n, 0, 10}]//Flatten CROSSREFS Triangles related to Eulerian numbers: A008292, A046802, A060187, A123125. Cf. A142175, A168287, A168288, A168289, A168290, A168291, A168292, A168293. Sequence in context: A039962 A046741 A136249 * A291977 A142073 A193559 Adjacent sequences:  A142144 A142145 A142146 * A142148 A142149 A142150 KEYWORD sign,tabf AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 15 2008 EXTENSIONS Edited, new name, and offset corrected by Franck Maminirina Ramaharo, Oct 21 2018 STATUS approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)