%I #14 Sep 25 2013 03:09:37
%S 1,1,3,7,35,139,1001,5701,53109,402985,4605271
%N Number of permutations of the numbers 1, 2, ..., n such that for all 1 <= k <= n the average of the first k numbers is at least the average of all n numbers.
%C Same as A147681.
%e For n = 3, the 3 permutations are (2,3,1), (3,1,2) and (3,2,1).
%o (PARI) a(n) = {nbok = 0; avg = (n+1)/2; for (j = 1, n!, perm = numtoperm(n, j); ok = 1; for (k = 1, n, if (sum(j=1, k, perm[j])/k < avg, ok = 0; break;);); if (ok, nbok++);); nbok;} \\ _Michel Marcus_, Aug 12 2013
%K nonn,more
%O 1,3
%A _N. Sato_, Oct 22 2008
%E a(7)-a(11) from _Michel Marcus_, Aug 12 2013