A396881 - OEIS

%I #5 Jun 09 2026 10:14:04

%S 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,

%T 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,

%U 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

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

%C 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.

%C 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.

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

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

%e 2.050597949676671019888931291256735847455656294562814...

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

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

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

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

%K nonn,cons

%O 1,1

%A _Amiram Eldar_, Jun 09 2026