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A360514
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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.
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4
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1, 1, 4, 9, 56, 185, 1632, 7217, 81664, 451089, 6241280, 41375609, 676506624, 5232134921, 98709925888, 872492313825, 18655203885056, 185503858236065, 4432984678858752, 48978641359097705, 1293646660855398400, 15722400263686662105, 454816628946740707328
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OFFSET
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1,3
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COMMENTS
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Bouwer and Star give a recurrence.
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REFERENCES
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Bouwer, I., and Z. Star. "A question of protocol." The American mathematical monthly 95.2 (1988): 118-121. See O(n).
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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