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 A293298 Triangle read by rows, a generalization of the Eulerian numbers based on Nielsen's generalized polylogarithm (case m = 3). 1
 1, 0, 1, 0, 1, -2, 0, 1, -5, 2, 0, 1, -10, 5, 0, 1, -19, 1, 11, 0, 1, -36, -46, 84, 19, 0, 1, -69, -272, 358, 393, 29, 0, 1, -134, -1149, 916, 4171, 1322, 41, 0, 1, -263, -4237, -191, 31939, 26255, 3841, 55, 0, 1, -520, -14536, -20192, 200252, 348848, 130924, 10280, 71 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Based on A142249 by Roger L. Bagula and Gary W. Adamson. LINKS Eric Weisstein's World of Mathematics, Nielsen Generalized Polylogarithm. FORMULA Let p(n, m) = (m - 1)!*(1 - x)^n*PolyLog(-n, m, x) and P(n) the polynomial given by the expansion of p(n, m=3) after replacing log(1 - x) by 1. T(n, k) is the k-th coefficient of P(n). EXAMPLE Triangle starts: {1} {0, 1} {0, 1,   -2} {0, 1,   -5,     2} {0, 1,  -10,     5} {0, 1,  -19,     1,   11} {0, 1,  -36,   -46,   84,    19} {0, 1,  -69,  -272,  358,   393,    29} {0, 1, -134, -1149,  916,  4171,  1322,   41} {0, 1, -263, -4237, -191, 31939, 26255, 3841, 55} MATHEMATICA npl[n_, m_] := (m-1)! (1 - x)^n PolyLog[-n, m, x]; A293298Row[0] := {1}; A293298Row[n_] := CoefficientList[FunctionExpand[npl[n, 3]], x] /. Log[1-x] -> 1; Table[A293298Row[n], {n, 0, 10}] // Flatten CROSSREFS A123125 (m=1), A142249 (m=2 with missing first column), this seq. (m=3). Sequence in context: A193471 A182931 A260615 * A079134 A175528 A163940 Adjacent sequences:  A293295 A293296 A293297 * A293299 A293300 A293301 KEYWORD sign,tabl AUTHOR Peter Luschny, Oct 11 2017 STATUS approved

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)