A381845 a(n) = denominator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ).

1, 1, 8, 48, 192, 3840, 46080, 322560, 10321920, 26542080, 1857945600, 11678515200, 1961990553600, 25505877196800, 1428329123020800, 42849873690624000, 8903869857792000, 46620662575398912000, 2634762720116736000, 31888533201572855808000, 196237127394294497280000

Offset: 1

Author

Stefano Spezia, Mar 12 2025

Keywords

• nonn
• frac

Examples

			1, 1, 7/8, 37/48, 133/192, 2431/3840, 27007/46080, 176761/322560, ...
		

Crossrefs

Cf. A061360, A061382, A143991 (conjectured numerators).

Programs

Mathematica

a[n_]:=Denominator[(E/Pi)Integrate[Cos[x]/(1 + x^2)^n,{x,-Infinity,Infinity}]]; Array[a,21]