A213620 Triangle read by rows, coefficients of the Euler polynomials E_{n}(x) times A006519(n+1) in descending order of powers.

1, 2, -1, 1, -1, 0, 4, -6, 0, 1, 1, -2, 0, 1, 0, 2, -5, 0, 5, 0, -1, 1, -3, 0, 5, 0, -3, 0, 8, -28, 0, 70, 0, -84, 0, 17, 1, -4, 0, 14, 0, -28, 0, 17, 0, 2, -9, 0, 42, 0, -126, 0, 153, 0, -31, 1, -5, 0, 30, 0, -126, 0, 255, 0, -155, 0, 4, -22, 0, 165, 0, -924

Offset: 0

Author

Peter Luschny, Jun 16 2012

Keywords

• sign
• tabl

Examples

			e(0,x) = 1,
e(1,x) = 2*x^1 - 1,
e(2,x) =   x^2 -   x^1,
e(3,x) = 4*x^3 - 6*x^2  + 1,
e(4,x) =   x^4 - 2*x^3  +   x^1,
e(5,x) = 2*x^5 - 5*x^4  + 5*x^2  - 1.
		

Programs

Maple

seq(seq(coeff(2^padic[ordp](i+1,2)*euler(i,x),x,i-j),j=0..i),i=0..11);

Mathematica

Table[ CoefficientList[ EulerE[n, x]*2^IntegerExponent[n+1, 2], x] // Reverse, {n, 0, 11}] // Flatten (* Jean-François Alcover, May 21 2013 *)