_N. J. A. Sloane (njas(AT)research.att.com), _, Jan 18 2009, Jan 19 2009

OEIS Server: https://oeis.org/edit/global/110

Tetrahedron of numbers T(i,j,k) = (i+2*j+3*k)!/(i!*j!*k!*2^j*6^k) read with entries in the order defined in A144625.

1, 1, 1, 1, 1, 3, 3, 4, 10, 10, 1, 6, 15, 15, 10, 60, 105, 70, 280, 280, 1, 10, 45, 105, 105, 20, 210, 840, 1260, 280, 2520, 6300, 2800, 15400, 15400, 1, 15, 105, 420, 945, 945, 35, 560, 3780, 12600, 17325, 840, 12600, 69300, 138600, 15400, 184800, 600600, 200200, 1401400, 1401400

0,6

The slice sums are given by A144416.

The n-th slice of the tetrahedrom consists of the terms T(i,j,k) with i+j+k = n.

Slices 0,1,2,3,4,5 are:

....................1

------------------

....................1

...................1.1

------------------

....................10

...................4.10

..................1.3..3

------------------

...................280

..................70.280

................10.60.105

...............1..6.15..15

------------------

..................15400

................2800.15400

...............280.2520.6300

.............20..210.840.1260

............1..10..45..105.105

------------------

.................1401400

.............200200.1401400

.........15400.184800...600600

......840..12600..69300...138600

...35....560....3780....12600...17325

1......15....105....420......945.....945

Cf. A144416, A144625, A144385.

nonn,tabf

N. J. A. Sloane (njas(AT)research.att.com), Jan 18 2009, Jan 19 2009

approved