A333273 - OEIS

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A333273

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

0

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

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OFFSET

1,3

COMMENTS

For Type A see A101280.

LINKS

Table of n, a(n) for n=1..41.

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.

FORMULA

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

EXAMPLE

Triangle begins:

1;

1, 4;

1, 20;

1, 72, 80;

1, 232, 976;

1, 716, 7664, 3904;

...

CROSSREFS

Cf. A101280, A008971. Row sums are A182825.

Sequence in context: A349708 A249716 A378511 * A128041 A144885 A144886

Adjacent sequences: A333270 A333271 A333272 * A333274 A333275 A333276

KEYWORD

nonn,tabf,changed

AUTHOR

N. J. A. Sloane, Mar 14 2020

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

STATUS

approved