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 A360514 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. 4
 1, 1, 4, 9, 56, 185, 1632, 7217, 81664, 451089, 6241280, 41375609, 676506624, 5232134921, 98709925888, 872492313825, 18655203885056, 185503858236065, 4432984678858752, 48978641359097705, 1293646660855398400, 15722400263686662105, 454816628946740707328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Bouwer and Star give a recurrence. REFERENCES Bouwer, I., and Z. Star. "A question of protocol." The American mathematical monthly 95.2 (1988): 118-121. See O(n). LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 PROG (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 CROSSREFS Cf. A360515, A360516, A360517. Sequence in context: A069507 A219894 A203464 * A358446 A152284 A109717 Adjacent sequences: A360511 A360512 A360513 * A360515 A360516 A360517 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 27 2023 EXTENSIONS Terms a(11) and beyond from Andrew Howroyd, Feb 27 2023 STATUS approved

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Last modified May 29 04:03 EDT 2023. Contains 363029 sequences. (Running on oeis4.)