A280841 Numerator of Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx / Pi.

1, 1, 1, 1727, 20652479, 2059268143, 24860948333867803, 145905074443586569379, 4567419249415312673370820607, 1642142815363470261591271553081, 4093745592094627817260334517735412136353665283

Offset

1,4

Comments

Let I(n) be defined by I(n) = Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx.

I(1) = I(2) = I(3) = Pi/2, however I(4) = Pi/2 - Pi/3456.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..15

Example

I(4) = 1727*Pi/3456. So a(4) = 1727.
I(5) = 20652479*Pi/41472000. So a(5) = 20652479.
I(6) = 2059268143*Pi/4147200000. So a(6) = 2059268143.
I(7) = 24860948333867803*Pi/50185433088000000. So a(7) = 24860948333867803.

Mathematica

f[n_] := Numerator[Integrate[Product[Sinc[x/k], {k, n}], {x, 0, Infinity}]/Pi]; Array[f, 11] (* Robert G. Wilson v, Jan 29 2017 *)

Crossrefs

Cf. A068214, A068215, A280842 (denominators).

Sequence in context: A031814 A020427 A232299 * A305474 A302142 A305494

Adjacent sequences: A280838 A280839 A280840 * A280842 A280843 A280844

Keyword

nonn,frac,more

Author

Seiichi Manyama, Jan 08 2017

Extensions

a(8)-a(11) from Alois P. Heinz, Jan 09 2017

Status

approved