A396881 Decimal expansion of Sum_{k>=0} (6^k)/(3*k)!.

2, 0, 5, 0, 5, 9, 7, 9, 4, 9, 6, 7, 6, 6, 7, 1, 0, 1, 9, 8, 8, 8, 9, 3, 1, 2, 9, 1, 2, 5, 6, 7, 3, 5, 8, 4, 7, 4, 5, 5, 6, 5, 6, 2, 9, 4, 5, 6, 2, 8, 1, 4, 4, 8, 1, 2, 2, 2, 7, 3, 9, 1, 6, 4, 1, 2, 0, 3, 9, 4, 7, 9, 2, 1, 2, 8, 7, 4, 1, 1, 9, 9, 8, 6, 6, 3, 1, 7, 4, 8, 7, 6, 4, 3, 2, 6, 5, 1, 2, 4, 2, 2, 5, 0, 0, 4

Offset

1,1

Comments

The expected number of points that are independently and uniformly selected at random in a unit ball until the sum of their distances from the center exceeds 1.

In general, the expected number of points that are independently and uniformly selected at random in a unit d-dimensional ball until the sum of their distances from the center exceeds 1, is Sum_{k>=0} ((d!)^k)/(d*k)!. The limit as d tends to infinity is 2.

Links

Table of n, a(n) for n=1..106.

Formula

Equals Sum_{k>=0} 1/A014606(k).

Equals (exp(6^(1/3)) + 2 * exp(-6^(1/3)/2) * cos(3^(5/6)/2^(2/3))) / 3.

Example

2.050597949676671019888931291256735847455656294562814...

Mathematica

RealDigits[(Exp[6^(1/3)] + 2 * Exp[-6^(1/3)/2] * Cos[3^(5/6)/2^(2/3)]) / 3, 10, 120][[1]]

Prog

(PARI) (exp(6^(1/3)) + 2 * exp(-6^(1/3)/2) * cos(3^(5/6)/2^(2/3))) / 3

Crossrefs

Cf. A000680, A014606, A014608, A014609, A248814, A172603, A172609, A172613.

Cf. A001113 (d=1), A395537 (d=2), this constant (d=3).

Sequence in context: A369907 A257013 A104755 * A242690 A054013 A048050

Adjacent sequences: A396878 A396879 A396880 * A396882 A396883 A396884

Keyword

nonn,cons

Author

Amiram Eldar, Jun 09 2026

Status

approved