A307132 Denominator of the expected fraction of occupied places on n-length lattice randomly filled with 2-length segments.

1, 3, 6, 5, 45, 63, 420, 405, 14175, 17325, 187110, 552825, 14189175, 49116375, 729729000, 723647925, 8881133625, 109185701625, 2062396586250, 10257709336875, 428772250281375, 2348038513445625, 53791427762572500, 160789593855515625, 16025362854266390625

Offset

1,2

Comments

The limit of expected fraction of occupied places on n-length lattice randomly filled with 2-length segments at n tends to infinity is equal to 1-1/e^2 (see A219863).

Links

Table of n, a(n) for n=1..25.

D. G. Radcliffe, Fat men sitting at a bar

Formula

Denominator of f(n), where f(0)=0; f(1)=0 and f(n) = (2 + 2(n-2)f(n-2) + (n-1)(n-2)f(n-1))/(n(n-1)) for n>1.

Example

0, 1, 2/3, 5/6, 4/5, 37/45, 52/63, 349/420, 338/405, 11873/14175, ...

Mathematica

RecurrenceTable[{f[n] == (2 + 2 (n - 2) f[n - 2] + (n - 1) (n - 2) f[n - 1])/(n (n - 1)), f[0] == 0, f[1] == 0}, f, {n, 2, 100}] // Denominator

Crossrefs

Cf. A219863, A231580, A307131 (numerators).

Sequence in context: A115389 A303564 A121867 * A300673 A335633 A009193

Adjacent sequences: A307129 A307130 A307131 * A307133 A307134 A307135

Keyword

nonn,frac

Author

Philipp O. Tsvetkov, Mar 26 2019

Status

approved