%I
%S 1,1,3,1,115,11,43141,733,722109,1093,143795597,47489,14249936103,
%T 5276161
%N Numerator of the rational coefficient at the first power of Pi in Sum_{k>0} (sin(k)/k)^n.
%e a(1) = 1, because Sum_{k>0} (sin(k)/k)^1 = (1/2)*Pi  1/2.
%e a(2) = 1, because Sum_{k>0} (sin(k)/k)^2 = (1/2)*Pi  1/2.
%e a(3) = 3, because Sum_{k>0} (sin(k)/k)^3 = (3/8)*Pi  1/2.
%e a(4) = 1, because Sum_{k>0} (sin(k)/k)^4 = (1/3)*Pi  1/2.
%e This simple pattern breaks starting at n = 7:
%e 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.
%t a[n_] := Numerator@Coefficient[Sum[Sinc[k]^n, {k, 1, Infinity}], Pi]
%Y Cf. A274041 (denominators).
%K sign,more,hard,frac
%O 1,3
%A _Vladimir Reshetnikov_, Jun 07 2016
