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A307132
Denominator of the expected fraction of occupied places on n-length lattice randomly filled with 2-length segments.
3
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).
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
KEYWORD
nonn,frac
AUTHOR
Philipp O. Tsvetkov, Mar 26 2019
STATUS
approved