A395628 a(n) = f(n+1) * n! where f(n) = n/f(n-1), f(1) = 1.

1, 2, 3, 16, 45, 384, 1575, 18432, 99225, 1474560, 9823275, 176947200, 1404728325, 29727129600, 273922023375, 6658877030400, 69850115960625, 1917756584755200, 22561587455281875, 690392370511872000, 9002073394657468125, 303772643025223680000, 4348001449619557104375, 160391955517318103040000, 2500100833531245335015625

Offset

0,2

Comments

Also, the inverse of the fraction where the numerator is (...(1/2)/3...)/n = 1/n! and the denominator is (n+1)/(n/(.../(2/1)...)), sometimes written in a diamond shape with each of the numbers as 1+...+1, cf. EXAMPLE.

Links

Paolo Xausa, Table of n, a(n) for n = 0..449

Formula

a(n) = (n+1)!*(n-1)! / a(n-1) for n > 0.

a(2n+1) = A002474(n).

Example

For n >= 1, the terms are the inverse of the fractions
  1      1        1                        1
----- = ---  ;   ---                      ---
 1+1     2       1+1      1/2     1       1+1
 ---           ------- = ----- = --- ;   -----
  1             1+1+1     3/2     3      1+1+1      (1/2)/3     1/6
                -----                  --------- = --------- = ----- = 1/16, etc.
                 1+1                    1+1+1+1     4/(3/2)     8/3
                 ---                    -------
                  1                      1+1+1
                                         -----
                                          1+1
                                          ---
                                           1

Mathematica

FoldList[(#2+1)!*(#2-1)!/# &, 1, Range[25]] (* Paolo Xausa, Jun 11 2026 *)

Prog

(PARI) apply( {A395628(n)=if(n<3, n+1, (n+1)!*(n-1)!/A395628(n-1))}, [0..20])

Crossrefs

Cf. A002474.

Sequence in context: A344747 A073633 A380950 * A012357 A012701 A012356

Adjacent sequences: A395625 A395626 A395627 * A395629 A395630 A395631

Keyword

nonn

Author

M. F. Hasler, Jun 05 2026

Status

approved