A060096 -id:A060096 - cp's OEIS frontend

A342314 T(n, k) = [x^k] 2^n*(Euler(n, x/2) + Euler(n, x)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.

2, -2, 3, 0, -6, 5, 4, 0, -15, 9, 0, 24, 0, -36, 17, -32, 0, 100, 0, -85, 33, 0, -288, 0, 360, 0, -198, 65, 544, 0, -1680, 0, 1190, 0, -455, 129, 0, 6528, 0, -8064, 0, 3696, 0, -1032, 257, -15872, 0, 48960, 0, -34272, 0, 10920, 0, -2313, 513, 0, -238080, 0, 293760, 0, -133056, 0, 30960, 0, -5130, 1025

Offset: 0

Peter Luschny, Mar 19 2021

			Table starts:
                             [0] 2
                           [1] -2, 3
                         [2] 0, -6, 5
                       [3] 4, 0, -15, 9
                     [4] 0, 24, 0, -36, 17
                  [5] -32, 0, 100, 0, -85, 33
               [6] 0, -288, 0, 360, 0, -198, 65
           [7] 544, 0, -1680, 0, 1190, 0, -455, 129
         [8] 0, 6528, 0, -8064, 0, 3696, 0, -1032, 257
   [9] -15872, 0, 48960, 0, -34272, 0, 10920, 0, -2313, 513

Cf. A060096/A060097, A163982 (row sums).

CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):
E := (n,x) -> 2^n*(euler(n, x/2) + euler(n, x));
seq(CoeffList(E(n, x)), n=0..9);

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.

Original entry on oeis.org

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

Peter Luschny, Mar 19 2021

			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

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

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);

cp's OEIS Frontend

A342314 T(n, k) = [x^k] 2^n*(Euler(n, x/2) + Euler(n, x)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.

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