A337354 a(n) is the numerator of Product_{i=0..n-1} (n-i)^((-1)^ceiling(i/2)).
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
Examples
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
Programs
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PARI
a(n) = {numerator(prod(i=0, n-1, (n-i)^(-1)^((i+1)\2)))} \\ Andrew Howroyd, Aug 24 2020
Formula
a(n) = numerator of (n*A337355(n-2))/(a(n-2)*(n-1)) for n>=3.
Extensions
Terms a(31) and beyond from Andrew Howroyd, Aug 25 2020
Comments