This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382709 #23 Jul 09 2025 05:09:00 %S A382709 0,1,3,21,45,465,2835,40005,80325,1448685,14501025,319178475, %T A382709 1915538625,49810085325,697383762075,20922151375125,41844941263125, %U A382709 1422738857665125,25609397130442125,973158947113728375,9731598751921921875,408727342477198119375,8992003678359610033125,413632218513350843881875 %N A382709 Numerator of (2^n - 1)*n! / 2^(n+1). %C A382709 The denominators (for n > 0) are A117973. %H A382709 Robert Israel, <a href="/A382709/b382709.txt">Table of n, a(n) for n = 0..448</a> %e A382709 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, ... %p A382709 f:= proc(n) numer((2^n-1)*n!/2^(n+1)) end proc: %p A382709 map(f, [$0..40]); # _Robert Israel_, Apr 06 2025 %t A382709 A382709[n_] := Numerator[(2^n - 1)*n!/2^(n + 1)]; %t A382709 Array[A382709, 25, 0] (* _Paolo Xausa_, Apr 07 2025 *) %Y A382709 Cf. A117973. %K A382709 nonn,frac %O A382709 0,3 %A A382709 _N. J. A. Sloane_, Apr 06 2025, following a suggestion from Fernando Galve Mauricio