%I #5 Oct 24 2012 21:03:54
%S 1,1,14,74,1363,13953,330628,5094436,148124741,3062897555,
%T 105624547606,2746180200462,109589993167831,3435877666633237,
%U 155759360424218888,5720220913807900808,290376774291325403401,12228041680671237910119,687155830301443577149594
%N Number of ordered n-tuples of positive integers such that the largest value is n and the first value is odd.
%H Alois P. Heinz, <a href="/A167633/b167633.txt">Table of n, a(n) for n = 1..150</a>
%F a(n) = [x^(n-1)] z/((n*x-1)*((n-1)*x-1)), where z = (n/2*x) if n is even, and z = (1-(n-1)/2*x) else.
%e a(3) = 14, because there are 14 ordered 3-tuples of positive integers such that the largest value is 3 and the first value is odd: 113, 123, 131, 132, 133, 311, 312, 313, 321, 322, 323, 331, 332, 333.
%p a:= n-> (Matrix (`if` (irem(n, 2)=0, [n/2, 0], [1 +(n-1)/2*3, 1])). Matrix ([[2*n-1, 1], [n*(1-n), 0]]) ^(n-1))[1, 2]: seq (a(n), n=1..20);
%Y Diagonal of A123685. Cf. A047969.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Nov 07 2009