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A343170 Triangle read by rows: coefficients of type B alternating Eulerian polynomials. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 24 11:34 EDT 2021. Contains 348225 sequences. (Running on oeis4.)