A333273 Irregular triangle read by rows: coefficients of q-Eulerian polynomials of Type B.

1, 1, 4, 1, 20, 1, 72, 80, 1, 232, 976, 1, 716, 7664, 3904, 1, 2172, 49776, 88640, 1, 6544, 292320, 1217792, 354560, 1, 19664, 1618656, 13201664, 12933376, 1, 59028, 8643872, 124784768, 274820352, 51733504, 1, 177124, 45108256, 1080946304, 4469939456, 2767631360

Offset: 1

Author

N. J. A. Sloane, Mar 14 2020

Keywords

• nonn
• tabf

Comments

For Type A see A101280.

Examples

			Triangle begins:
  1;
  1,    4;
  1,   20;
  1,   72,   80;
  1,  232,  976;
  1,  716, 7664, 3904;
  ...
		

Links

• Guoniu Han, Frédéric Jouhet, and Jiang Zeng, Two new triangles of q-integers via q-Eulerian polynomials of type A and B, preprint.
• Guoniu Han, Frédéric Jouhet, and Jiang Zeng, Two new triangles of q-integers via q-Eulerian polynomials of type A and B, Ramanujan J (2013) 31:115-127.

Crossrefs

Cf. A101280, A008971. Row sums are A182825.

Formula

T(n, k) = A008971(n, k) * 4^k. [Han et al.] - Andrey Zabolotskiy, Feb 15 2025

Extensions

Term T(6, 2) corrected (Table 1 in the Han et al. reference has a typo) by Robert S. Maier, Feb 15 2025

Rows 7-11 from Andrey Zabolotskiy, Mar 03 2025