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a(n) = A205497(2*n, n - 1). The central coefficients of the Eulerian zig-zag polynomials.
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%I #10 Jun 17 2024 07:56:35

%S 1,1,3,31,623,20641,1019051,70148989,6421463423,754405836811,

%T 110644077164479,19814920352425441,4255291684449288503,

%U 1079391696218976473971,319292229636452654327115,108942069149956119095870401,42469095372194594340983910271,18758916770545140042717283889713

%N a(n) = A205497(2*n, n - 1). The central coefficients of the Eulerian zig-zag polynomials.

%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.

%p 1, 1, seq(A205497row(2*n)[n], n = 2..17);

%Y Cf. A205497, A373755.

%K nonn

%O 0,3

%A _Peter Luschny_, Jun 16 2024