A141684 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)).

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, 0, -168, 0, 140, 0, -56, 16, 0, 17, 0, -28, 0, 14, 0, -4, 1, -496, 0, 2448, 0, -2016, 0, 672, 0, -144, 32, 0, -155, 0, 255, 0, -126, 0, 30, 0, -5, 1

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 08 2008

Keywords

• tabl
• sign

Comments

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

Examples

			{   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,    0, -168,   0,   140,    0, -56, 16},
{   0,   17,    0, -28,     0,   14,   0, -4,    1},
{-496,    0, 2448,   0, -2016,    0, 672,  0, -144, 32},
{   0, -155,    0, 255,     0, -126,   0, 30,    0, -5, 1}
		

Links

• G. C. Greubel, Rows n=1..100 of triangle, flattened

Crossrefs

Cf. A060083, A004172, etc.

Programs

Mathematica

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[%]

Extensions

Edited by N. J. A. Sloane, Jan 06 2009