A093533 Denominators of Pi * average length of a line segment picked at random in the unit n-ball for even n.

45, 4725, 35035, 34459425, 672188517, 16917875975, 935794913625, 1084960622856825, 6462226125730375, 274099062411663489, 24003893688766398225, 2225481769936755841875, 115326308912488315807725, 1132155423256546294315875, 9033912019628784618888327, 590708564889936682003293904425

Offset

1,1

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Ball Line Picking.

Wikipedia, Mean line segment length

Example

[2/3], 128/(45*Pi), [36/35], 16384/(4725*Pi), [800/693], 131072/(35035*Pi), [1568/1287], 134217728/(34459425*Pi), [290304/230945], ..., where the fractions [...] are for odd n. - modified by Hugo Pfoertner, Jan 19 2026

Prog

(PARI) betae(n) = 2^(3*n+1)*(n\2)!^2*n!/((n+1)*(2*n)!);
a093533(n) = my(m=2*n); denominator(2*m*betae(m)/(2*m+1)); \\ Hugo Pfoertner, Jan 19 2026

Crossrefs

Cf. A000796, A093530, A093531, A093532 (numerators).

Sequence in context: A328356 A375052 A384078 * A101291 A061542 A037182

Adjacent sequences: A093530 A093531 A093532 * A093534 A093535 A093536

Keyword

nonn,frac

Author

Eric W. Weisstein, Mar 30 2004

Extensions

More terms from Hugo Pfoertner, Jan 19 2026

Status

approved