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

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Formula

See the formulas in A380949.

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))):

Mathematica

Join[{1}, Denominator[FoldList[(#2 - 1)/(#2*#) &, Range[30]]]] (* Paolo Xausa, Feb 14 2025 *)

Crossrefs

Cf. A380949 (numerator).

Sequence in context: A072684 A344747 A073633 * A012357 A012701 A012356

Adjacent sequences: A380945 A380946 A380949 * A380955 A380956 A380957

Keyword

nonn,frac,new

Author

Peter Luschny, Feb 11 2025

Status

approved