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%I #10 Feb 27 2023 22:52:20
%S 1,1,4,9,56,185,1632,7217,81664,451089,6241280,41375609,676506624,
%T 5232134921,98709925888,872492313825,18655203885056,185503858236065,
%U 4432984678858752,48978641359097705,1293646660855398400,15722400263686662105,454816628946740707328
%N Number of 2-color vertex orderings of the labeled path graph on n vertices in which the number 1 is assigned to a vertex in an odd position.
%C Bouwer and Star give a recurrence.
%D Bouwer, I., and Z. Star. "A question of protocol." The American mathematical monthly 95.2 (1988): 118-121. See O(n).
%H Andrew Howroyd, <a href="/A360514/b360514.txt">Table of n, a(n) for n = 1..200</a>
%o (PARI) A360514seq(n) = {my(a=vector(n)); a[1]=a[2]=1; for(n=3, n, a[n] =(n-1) * if(n%2, 2*a[n-2], a[n-2] + (n-2)*a[n-3]) + 2*sum(k=1, (n-3)\2, binomial(n-1, 2*k) * k*(n-2*k-1)*a[2*k-1]*a[n-2*k-2])); a} \\ _Andrew Howroyd_, Feb 27 2023
%Y Cf. A360515, A360516, A360517.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Feb 27 2023
%E Terms a(11) and beyond from _Andrew Howroyd_, Feb 27 2023
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