login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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, 1, 2, 8, 33, 136, 670, 3968, 25593, 176896, 1344154, 11184128, 99897361, 951878656, 9687175862, 104932671488, 1202872541673, 14544442556416, 185158504589938, 2475749026562048, 34676498435503489, 507711943253426176, 7757079744889072462, 123460740095103991808
OFFSET
0,5
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.
FORMULA
MAPLE
enum := L -> ListTools:-Enumerate(L):
seq(add(c[2]*irem(c[1], 2), c = enum([A205497row(n)])), n = 0..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jun 16 2024
STATUS
approved