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

0,4

Links

Table of n, a(n) for n=0..44.

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

Example

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

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 *)

Crossrefs

Cf. A145876, A343171.

Sequence in context: A186102 A170848 A078017 * A169816 A291739 A057053

Adjacent sequences: A343167 A343168 A343169 * A343171 A343172 A343173

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 21 2021

Extensions

More terms from Jean-François Alcover, Apr 21 2021

Status

approved