A274041 Denominator of the rational coefficient at the first power of Pi in Sum_{k>0} (sin(k)/k)^n.

2, 2, 8, 3, 384, 40, 15360, 210, 1146880, 672, 137625600, 30800, 1153433600, 332800

Offset

1,1

Links

Table of n, a(n) for n=1..14.

Example

a(1) = 2, because Sum_{k>0} (sin(k)/k)^1 = (1/2)*Pi - 1/2.
a(2) = 2, because Sum_{k>0} (sin(k)/k)^2 = (1/2)*Pi - 1/2.
a(3) = 8, because Sum_{k>0} (sin(k)/k)^3 = (3/8)*Pi - 1/2.
a(4) = 3, because Sum_{k>0} (sin(k)/k)^4 = (1/3)*Pi - 1/2.
This simple pattern breaks starting at n = 7:
a(7) = 15360, because Sum_{k>0} (sin(k)/k)^7 = (1/720)*Pi^7 - (7/240)*Pi^6 + (49/192)*Pi^5 - (343/288)*Pi^4 + (2401/768)*Pi^3 - (16807/3840)*Pi^2 + (43141/15360)*Pi - 1/2.

Mathematica

a[n_] := Denominator@Coefficient[Sum[Sinc[k]^n, {k, 1, Infinity}], Pi]

Crossrefs

Cf. A274040 (numerators).

Sequence in context: A143440 A093731 A195361 * A049331 A369771 A239677

Adjacent sequences: A274038 A274039 A274040 * A274042 A274043 A274044

Keyword

nonn,more,hard,frac

Author

Vladimir Reshetnikov, Jun 07 2016

Status

approved