A343170 Triangle read by rows: coefficients of type B alternating Eulerian polynomials.

1, 1, 1, 3, 2, 3, 11, 13, 13, 11, 57, 76, 118, 76, 57, 361, 597, 962, 962, 597, 361, 2763, 5270, 9733, 10548, 9733, 5270, 2763, 24611, 53849, 107427, 136673, 136673, 107427, 53849, 24611, 250737, 616408, 1334556, 1875432, 2167654, 1875432, 1334556, 616408, 250737

Offset: 0

Author

N. J. A. Sloane, Apr 21 2021

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1;
   1,  1;
   3,  2,   3;
  11, 13,  13, 11;
  57, 76, 118, 76, 57;
  ...
		

Links

• Shi-Mei Ma, Qi Fang, Toufik Mansour and Yeong-Nan Yeh, Alternating Eulerian polynomials and left peak polynomials, arXiv:2104.09374 [math.CO], 2021.

Crossrefs

Cf. A145876, A343171.

Programs

Mathematica

Bhat[0][] = 1; Bhat[1][x] := 1 + x;
Bhat[n_][x_] := Bhat[n][x] = (n + x + (n-1) x^2) Bhat[n - 1][x] + (1 - x)* (1 + x^2) Bhat[n-1]'[x];
Table[CoefficientList[Bhat[n][x], x], {n, 0, 8}] // Flatten (* Jean-François Alcover, Apr 21 2021 *)

Extensions

More terms from Jean-François Alcover, Apr 21 2021