A249769 Sequence of distinct least positive numbers such that the average of the first n terms is a factorial.

1, 3, 2, 18, 6, 114, 24, 792, 120, 6120, 720, 52560, 5040, 498960, 40320, 5201280, 362880, 59149440, 3628800, 729388800, 39916800, 9699782400, 479001600, 138431462400, 6227020800, 2110960051200, 87178291200, 34261068441600, 1307674368000, 589761139968000, 20922789888000

Offset

1,2

Links

Table of n, a(n) for n=1..31.

Formula

a(2*n-1) = n!.

a(2*n) = n!*(2*n^2+1).

Prog

(PARI) v=[]; n=0; while(n<10^7, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=0, n, if(i!>(num/(#v+1)), break); if(i!==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=0; break))); n++)

Crossrefs

Sequence in context: A361084 A158939 A173795 * A026345 A092644 A006281

Adjacent sequences: A249766 A249767 A249768 * A249770 A249771 A249772

Keyword

nonn

Author

Derek Orr, Nov 05 2014

Status

approved