A373753 a(n) = Sum_{k=0..n-2} A205497(n, k) * (k mod 2).

0, 0, 0, 1, 3, 8, 28, 136, 715, 3968, 24928, 176896, 1358611, 11184128, 99463620, 951878656, 9704336283, 104932671488, 1202007133768, 14544442556416, 185212683647587, 2475749026562048, 34672375957634412, 507711943253426176, 7757454418668014443, 123460740095103991808

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..25.

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

Formula

a + A373752 = A000111.

Maple

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

Crossrefs

Cf. A205497, A000111, A373752.

Sequence in context: A000776 A327030 A355986 * A000239 A268302 A345177

Adjacent sequences: A373750 A373751 A373752 * A373754 A373755 A373756

Keyword

nonn

Author

Peter Luschny, Jun 16 2024

Status

approved