Original entry on oeis.org
3, 19, 80, 286, 945, 2997, 9294, 28456, 86471, 261559, 788892, 2375010, 7141581, 21457705, 64438874, 193447948, 580606275, 1742343435, 5228079240, 15686335270, 47063200553, 141197990749, 423610749990, 1270865804976, 3812664524415, 11438127791647
Offset: 3
-
Table[(CoefficientList[Simplify[(1-x)^n * PolyLog[-n, 2, x] / (x*Log[1-x])], x]/.x->1-E)[[3]], {n, 4, 20}]
Original entry on oeis.org
4, 65, 566, 3710, 20756, 105299, 500862, 2278936, 10046620, 43280341, 183278902, 766153042, 3171277460, 13027450455, 53203165950, 216290270892, 876183166140, 3539559610905, 14267986165270, 57416955957350, 230750092893524, 926388737476955, 3716144413352126
Offset: 4
-
Table[(CoefficientList[Simplify[(1-x)^n * PolyLog[-n, 2, x] / (x*Log[1-x])], x]/.x->1-E)[[4]], {n, 5, 20}]
A293298
Triangle read by rows, a generalization of the Eulerian numbers based on Nielsen's generalized polylogarithm (case m = 3).
Original entry on oeis.org
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
Offset: 0
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}
A123125 (m=1),
A142249 (m=2 with missing first column), this seq. (m=3).
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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
Showing 1-3 of 3 results.
Comments