A167633 Number of ordered n-tuples of positive integers such that the largest value is n and the first value is odd.

1, 1, 14, 74, 1363, 13953, 330628, 5094436, 148124741, 3062897555, 105624547606, 2746180200462, 109589993167831, 3435877666633237, 155759360424218888, 5720220913807900808, 290376774291325403401, 12228041680671237910119, 687155830301443577149594

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..150

Formula

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.

Example

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.

Maple

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);

Crossrefs

Diagonal of A123685. Cf. A047969.

Sequence in context: A232377 A146563 A205583 * A196411 A108650 A093567

Adjacent sequences: A167630 A167631 A167632 * A167634 A167635 A167636

Keyword

nonn

Author

Alois P. Heinz, Nov 07 2009

Status

approved