A141684 - OEIS

%I #13 Dec 29 2023 10:28:28

%S 1,-1,2,0,-1,1,1,0,-6,4,0,1,0,-2,1,-4,0,20,0,-20,8,0,-3,0,5,0,-3,1,34,

%T 0,-168,0,140,0,-56,16,0,17,0,-28,0,14,0,-4,1,-496,0,2448,0,-2016,0,

%U 672,0,-144,32,0,-155,0,255,0,-126,0,30,0,-5,1

%N Triangle read by rows formed from Euler polynomials: p(x,n) = if(n mod 2 = 1, 2^(1 + ((n - 1)/2))*EulerE(n, x), EulerE(n, x)); t(n,m) = Coefficients(p(x,n)).

%C Row sums are {1, 1, 0, -1, 0, 4, 0, -34, 0, 496, 0, ...}.

%H G. C. Greubel, <a href="/A141684/b141684.txt">Rows n=1..100 of triangle, flattened</a>

%e {   1},

%e {  -1,    2},

%e {   0,   -1,    1},

%e {   1,    0,   -6,   4},

%e {   0,    1,    0,  -2,     1},

%e {  -4,    0,   20,   0,   -20,    8},

%e {   0,   -3,    0,   5,     0,   -3,   1},

%e {  34,    0, -168,   0,   140,    0, -56, 16},

%e {   0,   17,    0, -28,     0,   14,   0, -4,    1},

%e {-496,    0, 2448,   0, -2016,    0, 672,  0, -144, 32},

%e {   0, -155,    0, 255,     0, -126,   0, 30,    0, -5, 1}

%t T[x_, n_] := If[Mod[n, 2] == 1, 2^(1 + ((n - 1)/2))*EulerE[n, x], EulerE[n, x]]; Table[Expand[T[x, n]], {n, 0, 10}]; Table[CoefficientList[T[x, n], x], {n, 0, 10}]; Flatten[%]

%Y Cf. A060083, A004172, etc.

%K tabl,sign

%O 1,3

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 08 2008

%E Edited by _N. J. A. Sloane_, Jan 06 2009