A375518 First differences of A375516.

1, 2, 8, 36, 1152, 240000, 9696240000, 11752718457744180000, 15347376819435640459450549232576160000, 23554197523775043569951631809272942030408567274885169881327076295276944000

Offset: 0

Author

N. J. A. Sloane, Aug 25 2024

Keywords

• nonn

Comments

The terms of A375516 are not well-understood. The present sequence was suggested by the fact that, from a certain point on, the terms of A375516 end with the digits 1200. If powers of 2 and 3 are ignored, the terms of the present sequence appear to be perfect squares.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..12

Crossrefs

Cf. A374663, A374983, A375516, A375517.

Programs

Maple

s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:
b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:
a:= n-> denom(s(n+1))-denom(s(n)):
seq(a(n), n=0..10);  # Alois P. Heinz, Oct 19 2024

Mathematica

s[n_] := s[n] = If[n == 0, 0, s[n - 1] + 1/(n*b[n])];
b[n_] := b[n] = 1 + Floor[1/((1 - s[n - 1])*n)];
a[n_] := Denominator[s[n + 1]] - Denominator[s[n]];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Feb 14 2025, after Alois P. Heinz *)

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 19 2024