%I #14 Oct 11 2017 19:43:17
%S 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,
%T -69,-272,358,393,29,0,1,-134,-1149,916,4171,1322,41,0,1,-263,-4237,
%U -191,31939,26255,3841,55,0,1,-520,-14536,-20192,200252,348848,130924,10280,71
%N Triangle read by rows, a generalization of the Eulerian numbers based on Nielsen's generalized polylogarithm (case m = 3).
%C Based on A142249 by _Roger L. Bagula_ and _Gary W. Adamson_.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NielsenGeneralizedPolylogarithm.html">Nielsen Generalized Polylogarithm</a>.
%F 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).
%e Triangle starts:
%e {1}
%e {0, 1}
%e {0, 1, -2}
%e {0, 1, -5, 2}
%e {0, 1, -10, 5}
%e {0, 1, -19, 1, 11}
%e {0, 1, -36, -46, 84, 19}
%e {0, 1, -69, -272, 358, 393, 29}
%e {0, 1, -134, -1149, 916, 4171, 1322, 41}
%e {0, 1, -263, -4237, -191, 31939, 26255, 3841, 55}
%t npl[n_, m_] := (m-1)! (1 - x)^n PolyLog[-n, m, x];
%t A293298Row[0] := {1};
%t A293298Row[n_] := CoefficientList[FunctionExpand[npl[n, 3]], x] /. Log[1-x] -> 1;
%t Table[A293298Row[n], {n, 0, 10}] // Flatten
%Y A123125 (m=1), A142249 (m=2 with missing first column), this seq. (m=3).
%K sign,tabl
%O 0,6
%A _Peter Luschny_, Oct 11 2017