OFFSET
1,3
EXAMPLE
a(1) = 1, because Sum_{k>0} (sin(k)/k)^1 = (1/2)*Pi - 1/2.
a(2) = 1, because Sum_{k>0} (sin(k)/k)^2 = (1/2)*Pi - 1/2.
a(3) = 3, because Sum_{k>0} (sin(k)/k)^3 = (3/8)*Pi - 1/2.
a(4) = 1, because Sum_{k>0} (sin(k)/k)^4 = (1/3)*Pi - 1/2.
This simple pattern breaks starting at n = 7:
a(7) = 43141, 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_] := Numerator@Coefficient[Sum[Sinc[k]^n, {k, 1, Infinity}], Pi]
CROSSREFS
KEYWORD
sign,more,hard,frac
AUTHOR
Vladimir Reshetnikov, Jun 07 2016
STATUS
approved