A382709 Numerator of (2^n - 1)*n! / 2^(n+1).

0, 1, 3, 21, 45, 465, 2835, 40005, 80325, 1448685, 14501025, 319178475, 1915538625, 49810085325, 697383762075, 20922151375125, 41844941263125, 1422738857665125, 25609397130442125, 973158947113728375, 9731598751921921875, 408727342477198119375, 8992003678359610033125, 413632218513350843881875

Offset: 0

Author

N. J. A. Sloane, Apr 06 2025, following a suggestion from Fernando Galve Mauricio

Keywords

• nonn
• frac

Comments

The denominators (for n > 0) are A117973.

Examples

			The fractions are 0, 1/4, 3/4, 21/8, 45/4, 465/8, 2835/8, 40005/16, 80325/4, 1448685/8, 14501025/8, 319178475/16, 1915538625/8, 49810085325/16, 697383762075/16, ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..448

Crossrefs

Cf. A117973.

Programs

Maple

f:= proc(n) numer((2^n-1)*n!/2^(n+1)) end proc:
map(f, [$0..40]); # Robert Israel, Apr 06 2025

Mathematica

A382709[n_] := Numerator[(2^n - 1)*n!/2^(n + 1)];
Array[A382709, 25, 0] (* Paolo Xausa, Apr 07 2025 *)