A105658 a(n) = (Product_{i=1..n} i^i) / denominator( Sum_{j=1..n} j*(j+1)/2 / (Product_{k=0..j-1} j!/k!) ).

1, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 143, 7, 15, 104, 935, 9, 19, 10, 21, 11, 4025, 3900, 325, 3289, 27, 14, 29, 15, 31, 368, 33, 17, 35, 18, 185, 19, 39, 380, 451, 399, 215, 770, 45, 23, 29563, 24, 12397, 725, 51, 26, 1537, 837, 2365, 1036, 285, 377, 2537, 30

Offset

0,4

Comments

Most of the time a(2n-1)=2n-1, but a(2n-1)!=2n-1 for 2n-1 = 13,17,23,25,37,41,43,47,49,53,55,57,59,61,63,...

Most of the time a(2n)=n, but a(2n)!=n for 2n = 16,24,26,32,40,42,44,50,54,56,58,64,84,86,96,100,102,104,...

Links

Table of n, a(n) for n=0..60.

Example

a(3) = 108/36 = 3.

Mathematica

f[n_] := Product[k^k, {k, 1, n}]/ Denominator[Sum[i(i + 1)/2/Product[i!/j!, {j, 0, i - 1}], {i, n}]]; Table[ f[n], {n, 0, 61}] (* Robert G. Wilson v, Apr 18 2005 *)

Prog

(PARI) a(n) = prod(i=1, n, i^i) / denominator(sum(j=1, n, j*(j+1)/2 / prod(k=0, j-1, j!/k!))) \\ Jason Yuen, Jan 18 2025

Crossrefs

Cf. A002109 (hyperfactorial numbers).

Sequence in context: A176447 A145051 A026741 * A083242 A111618 A107128

Adjacent sequences: A105655 A105656 A105657 * A105659 A105660 A105661

Keyword

nonn

Author

Jess E. Boling (tdbpeekitup(AT)yahoo.com), Apr 17 2005

Extensions

Edited by Robert G. Wilson v, Apr 18 2005

Name corrected by Jason Yuen, Jan 18 2025

Status

approved