

A274041


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


1



2, 2, 8, 3, 384, 40, 15360, 210, 1146880, 672, 137625600, 30800, 1153433600, 332800
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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 A239677 A331333
Adjacent sequences: A274038 A274039 A274040 * A274042 A274043 A274044


KEYWORD

nonn,more,hard,frac


AUTHOR

Vladimir Reshetnikov, Jun 07 2016


STATUS

approved



