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A360515
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 even position.
4
0, 1, 2, 9, 24, 185, 720, 7217, 35840, 451089, 2741760, 41375609, 297133056, 5232134921, 43356465152, 872492313825, 8193895956480, 185503858236065, 1947095049830400, 48978641359097705, 568206904265277440, 15722400263686662105, 199768581446090883072
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 E(n).
LINKS
FORMULA
a(2*n) = A360514(2*n); a(2*n+1) = 2*n*(2*n + 1)*A360514(2*n - 1) - A360514(2*n + 1) for n >= 1.
PROG
(PARI) \\ Needs A360514seq from A360514.
seq(n) = {my(v=A360514seq(n)); vector(#v, n, if(n%2, if(n==1, 0, (n-1)*n*v[n-2]-v[n]), v[n]))} \\ Andrew Howroyd, Feb 27 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 27 2023
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Feb 27 2023
STATUS
approved