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A108552 Integer values of (1*2*...*n)/(1+2+...+n) = n!/T(n) = A000142(n)/A000217(n), n>=1. 4
1, 1, 8, 180, 1120, 8064, 604800, 68428800, 830269440, 10897286400, 2324754432000, 640237370572800, 11585247657984000, 221172909834240000, 93666727314800640000, 2068161339110798131200, 47726800133326110720000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Factorial numbers (*) and triangular numbers (+) both operate on 1,2,...,n. A000142(n)/A000217(n) = n!/(n*(n+1)/2) = 2*(n-1)!/(n+1) is an integer iff n = 1 or n + 1 is composite; i.e., iff n is a term of A060462.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(m) = 2*(A060462(m)-1)!/(A060462(m)+1) = A000142(A060462(m))/A000217(A060462(m)), m>=0.

MATHEMATICA

Select[Table[(n - 1)!/((n (n - 1))/2), {n, 2, 50}], IntegerQ[#] &] (* Geoffrey Critzer, May 02 2015 *)

PROG

(PARI) for(n=1, 50, r=2*(n-1)!/(n+1); if(denominator(r)==1, print1(r, ", ")))

CROSSREFS

Cf. A060462 (corresponding n), A000142 (factorials), A000217 (triangular numbers).

Sequence in context: A299742 A299662 A300255 * A221589 A317486 A060593

Adjacent sequences:  A108549 A108550 A108551 * A108553 A108554 A108555

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Jun 09 2005

STATUS

approved

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Last modified June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)