A373752 a(n) = Sum_{k=0..n-2} A205497(n, k) * (1 - k mod 2) if n >= 2, a(0) = a(1) = 1.

1, 1, 1, 1, 2, 8, 33, 136, 670, 3968, 25593, 176896, 1344154, 11184128, 99897361, 951878656, 9687175862, 104932671488, 1202872541673, 14544442556416, 185158504589938, 2475749026562048, 34676498435503489, 507711943253426176, 7757079744889072462, 123460740095103991808

Offset: 0

Author

Peter Luschny, Jun 16 2024

Keywords

• nonn

Comments

Number of linear extensions in L(eps Z_n) that have an even number of descents. (See Petersen and Yan Zhuang, p. 6.)

Links

• T. Kyle Petersen and Yan Zhuang, Zig-zag Eulerian polynomials, arXiv:2403.07181 [math.CO], 2024.

Crossrefs

Cf. A205497, A000111, A373753.

Programs

Maple

enum := L -> ListTools:-Enumerate(L):
seq(add(c[2]*irem(c[1], 2), c = enum([A205497row(n)])), n = 0..25);

Formula

a + A373753 = A000111.