A380950 a(n) = denominator(r(n)) where r(n) = (n/2)*(Pi/2)^cos(Pi*(n-1))*((n/2-1/2)!/(n/2)!)^2.
1, 1, 2, 3, 16, 45, 128, 175, 2048, 11025, 32768, 43659, 262144, 693693, 2097152, 2760615, 67108864, 703956825, 2147483648, 2807136475, 17179869184, 44801898141, 137438953472, 178837328943, 2199023255552, 11425718238025, 35184372088832, 45635265151875, 281474976710656
Offset: 0
Links
- Paolo Xausa, Table of n, a(n) for n = 0..1000
Crossrefs
Cf. A380949 (numerator).
Programs
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Maple
r := n -> (n/2)*(Pi/2)^cos(Pi*(n-1))*((n/2-1/2)!/(n/2)!)^2: a := n -> denom(simplify(r(n))): seq(a(n), n = 0..28); # Alternative: r := n -> ifelse(n <= 1, n, (n - 1)/(n*r(n - 1))):
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Mathematica
Join[{1}, Denominator[FoldList[(#2 - 1)/(#2*#) &, Range[30]]]] (* Paolo Xausa, Feb 14 2025 *)
Formula
See the formulas in A380949.