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A373753
a(n) = Sum_{k=0..n-2} A205497(n, k) * (k mod 2).
1
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
T. Kyle Petersen and Yan Zhuang, Zig-zag Eulerian polynomials, arXiv:2403.07181 [math.CO], 2024.
FORMULA
MAPLE
enum := L -> ListTools:-Enumerate(L):
seq(add(c[2]*(1-irem(c[1], 2)), c = enum([A205497row(n)])), n = 0..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jun 16 2024
STATUS
approved