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

1,2

Comments

a(n) is the numerator of (n/(n-1)) * ((n-3)/(n-2)) * ((n-4)/(n-5)) ...

Links

Table of n, a(n) for n=1..40.

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).

Cf. A076390, A085565, A007662.

Sequence in context: A079535 A367859 A349789 * A293944 A050159 A147294

Adjacent sequences: A337351 A337352 A337353 * A337355 A337356 A337357

Keyword

nonn,frac

Author

Devansh Singh, Aug 24 2020

Extensions

Terms a(31) and beyond from Andrew Howroyd, Aug 25 2020

Status

approved