A338375 Number of digits in (2n)! / (2^n * n!).

1, 1, 2, 3, 3, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 19, 21, 22, 24, 26, 27, 29, 31, 32, 34, 36, 37, 39, 41, 43, 45, 46, 48, 50, 52, 54, 56, 58, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 104, 106, 108, 110

Offset: 1

Author

Jeremias M. Gomes, Oct 23 2020

Keywords

• nonn
• base

Comments

a(n) is the number of digits in double factorial of odd numbers (see A001147).

Examples

			For n = 7, (2*n-1)!! = 13!! = 135135 and the number of digits is 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001147, A055642, A068398.

Programs

Maple

seq(1 + ilog10(doublefactorial(2*n-1)), n=1..100); # Robert Israel, Jan 15 2024

Mathematica

a[n_] := IntegerLength[(2 n - 1)!!]; Array[a, 65] (* Amiram Eldar, Oct 23 2020 *)

Sage

floor((log(factorial(2 * n) / ((2 ** n) * factorial(n))) / log(10))) + 1

Formula

a(n) = floor(log((2n)!/((2^n)*n!))/log(10))+1.

a(n) = A055642(A001147(n)).