A342315 T(n, k) = [x^k] 2^n*(Euler(n, x) - Euler(n, x/2)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.

0, 0, 1, 0, -2, 3, 0, 0, -9, 7, 0, 8, 0, -28, 15, 0, 0, 60, 0, -75, 31, 0, -96, 0, 280, 0, -186, 63, 0, 0, -1008, 0, 1050, 0, -441, 127, 0, 2176, 0, -6272, 0, 3472, 0, -1016, 255, 0, 0, 29376, 0, -30240, 0, 10584, 0, -2295, 511, 0, -79360, 0, 228480, 0, -124992, 0, 30480, 0, -5110, 1023

Offset: 0

Author

Peter Luschny, Mar 19 2021

Keywords

• sign
• tabl

Examples

			Table starts:
                            [0] 0
                           [1] 0, 1
                         [2] 0, -2, 3
                        [3] 0, 0, -9, 7
                     [4] 0, 8, 0, -28, 15
                   [5] 0, 0, 60, 0, -75, 31
                [6] 0, -96, 0, 280, 0, -186, 63
            [7] 0, 0, -1008, 0, 1050, 0, -441, 127
         [8] 0, 2176, 0, -6272, 0, 3472, 0, -1016, 255
      [9] 0, 0, 29376, 0, -30240, 0, 10584, 0, -2295, 511
		

Crossrefs

Cf. A060096/A060097, A163747 (row sums).

Programs

Maple

CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):
E := (n, x) -> 2^n*(euler(n, x) - euler(n, x/2));
0,seq(CoeffList(E(n, x)), n = 0..10);