login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Denominators of n-th approximation of factorial (also called harmonic) expansion of Pi.
1

%I #7 Jan 28 2025 08:38:08

%S 1,1,1,8,15,720,5040,13440,13440,3628800,532224,43545600,691891200,

%T 691891200,108972864000,1902071808000,118562476032000,6847458508800,

%U 24329020081766400,17888985354240000,1344498478202880000

%N Denominators of n-th approximation of factorial (also called harmonic) expansion of Pi.

%C Numerators are given in A131445.

%C For the rationals r(n) and some values see the W. Lang link under A131445.

%F a(n) = denominator(r(n)), with r(n):=sum(b(k)/k!,n=1..n) with b(k):=A075874(k) (factorial expansion of Pi).

%e Rationals r(n): [3,3,3,25/8,47/15,2261/720,15833/5040,42223/13440,42223/13440,...].

%Y Cf. A000796, A131445.

%K nonn,frac,easy,changed

%O 1,4

%A _Wolfdieter Lang_, Aug 07 2007