A375532 a(n) is the denominator of Sum_{k = 1..n} k! / A375531(k).

1, 2, 10, 610, 8931010, 9571552763343010, 65962528057050631782397012182615010, 21929317742693046651753716375301870159888977066122278116986745673775119010

Offset: 0

Author

N. J. A. Sloane, Sep 04 2024

Keywords

• nonn
• frac

Examples

			The first few sums are 0/1, 1/2, 9/10, 609/610, 8931009/8931010, 9571552763343009/9571552763343010, ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Cf. A000142, A374663, A374983/A375516, A375531.

Programs

Maple

s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+n!/b(n)) end:
b:= proc(n) b(n):= 1+floor(n!/(1-s(n-1))) end:
a:= n-> denom(s(n)):
seq(a(n), n=0..7);  # Alois P. Heinz, Oct 18 2024

Mathematica

s[n_] := s[n] = If[n == 0, 0, s[n-1] + n!/b[n]];
b[n_] := b[n] = 1 + Floor[n!/(1 - s[n-1])];
a[n_] := Denominator[s[n]];
Table[a[n], {n, 0, 7}] (* Jean-François Alcover, Dec 10 2024, after Alois P. Heinz *)

Formula

a(n+1) = (n+1)!*a(n)^2 + a(n), with a(1) = 2.

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 18 2024