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A337354
a(n) is the numerator of Product_{i=0..n-1} (n-i)^((-1)^ceiling(i/2)).
1
1, 2, 3, 2, 5, 9, 7, 40, 45, 7, 308, 48, 975, 539, 88, 1664, 1105, 24255, 13376, 56576, 41769, 48279, 55936, 226304, 348075, 370139, 671232, 870400, 2082925, 4283037, 13872128, 80773120, 343682625, 4023459, 1553678336, 1900544, 14411758075, 59457783, 1471905792, 1406402560
OFFSET
1,2
COMMENTS
a(n) is the numerator of (n/(n-1)) * ((n-3)/(n-2)) * ((n-4)/(n-5)) ...
FORMULA
a(n) = numerator of (n*A337355(n-2))/(a(n-2)*(n-1)) for n>=3.
Conjecture: a(4*n)/A337355(4*n) ~ 0.5990701173677... (=A076390). - Andrew Howroyd, Aug 25 2020
EXAMPLE
a(n)/A337355(n) equals 1, 2, 3/2, 2/3, 5/6, 9/5, 7/5, 40/63, 45/56, 7/4 ...
a(4) = numerator of (4*1)/(3*2) = numerator of 2/3 = 2.
a(5) = numerator of (5*2)/(4*3) = numerator of 5/6 = 5.
12 * 9*8 * 5*4 * 1
a(12) = numerator of --------------------------- = 48.
11*10 * 7*6 * 3*2
PROG
(PARI) a(n) = {numerator(prod(i=0, n-1, (n-i)^(-1)^((i+1)\2)))} \\ Andrew Howroyd, Aug 24 2020
CROSSREFS
Cf. A337355 (denominators).
Sequence in context: A079535 A367859 A349789 * A293944 A050159 A147294
KEYWORD
nonn,frac
AUTHOR
Devansh Singh, Aug 24 2020
EXTENSIONS
Terms a(31) and beyond from Andrew Howroyd, Aug 25 2020
STATUS
approved