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%I #10 Jun 17 2024 07:56:26
%S 1,1,1,1,2,8,33,136,670,3968,25593,176896,1344154,11184128,99897361,
%T 951878656,9687175862,104932671488,1202872541673,14544442556416,
%U 185158504589938,2475749026562048,34676498435503489,507711943253426176,7757079744889072462,123460740095103991808
%N a(n) = Sum_{k=0..n-2} A205497(n, k) * (1 - k mod 2) if n >= 2, a(0) = a(1) = 1.
%C Number of linear extensions in L(eps Z_n) that have an even number of descents. (See Petersen and Yan Zhuang, p. 6.)
%H T. Kyle Petersen and Yan Zhuang, <a href="https://arxiv.org/abs/2403.07181">Zig-zag Eulerian polynomials</a>, arXiv:2403.07181 [math.CO], 2024.
%F a + A373753 = A000111.
%p enum := L -> ListTools:-Enumerate(L):
%p seq(add(c[2]*irem(c[1], 2), c = enum([A205497row(n)])), n = 0..25);
%Y Cf. A205497, A000111, A373753.
%K nonn
%O 0,5
%A _Peter Luschny_, Jun 16 2024