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A167633 Number of ordered n-tuples of positive integers such that the largest value is n and the first value is odd. 1
1, 1, 14, 74, 1363, 13953, 330628, 5094436, 148124741, 3062897555, 105624547606, 2746180200462, 109589993167831, 3435877666633237, 155759360424218888, 5720220913807900808, 290376774291325403401, 12228041680671237910119, 687155830301443577149594 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 20 22:20 EDT 2019. Contains 325189 sequences. (Running on oeis4.)