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.

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

Andrew Howroyd, Table of n, a(n) for n = 1..200

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

Cf. A360514, A360516, A360517.

Sequence in context: A097346 A343576 A261431 * A226388 A053194 A346069

Adjacent sequences: A360512 A360513 A360514 * A360516 A360517 A360518

Keyword

nonn

Author

N. J. A. Sloane, Feb 27 2023

Extensions

Terms a(11) and beyond from Andrew Howroyd, Feb 27 2023

Status

approved