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A274040
Numerator of the rational coefficient at the first power of Pi in Sum_{k>0} (sin(k)/k)^n.
1
1, 1, 3, 1, 115, 11, 43141, 733, -722109, -1093, 143795597, 47489, 14249936103, 5276161
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
Cf. A274041 (denominators).
Sequence in context: A221195 A071291 A049330 * A367948 A369187 A266363
KEYWORD
sign,more,hard,frac
AUTHOR
STATUS
approved