A105658 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A105658

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

(list; graph; refs; listen; history; text; internal format)

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 *)

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

STATUS

approved