A280842 Denominator of Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx / Pi.

2, 2, 2, 3456, 41472000, 4147200000, 50185433088000000, 295090346557440000000, 9251918060437194670080000000, 3330690501757390081228800000000, 8312243866372850396258184884618526720000000000

Offset: 1

Author

Seiichi Manyama, Jan 08 2017

Keywords

• nonn
• frac
• more

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.

Examples

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

Links

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

Crossrefs

Cf. A068214, A068215, A280841 (numerators).

Programs

Mathematica

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

Extensions

a(8)-a(11) from Alois P. Heinz, Jan 10 2017