A181417 Irregular triangle T(n,k) = binomial(n-1,m-1)*m!*A036040(n,k), where m=A036043(n,k).

1, 1, 2, 1, 12, 6, 1, 24, 18, 108, 24, 1, 40, 80, 360, 540, 960, 120, 1, 60, 150, 100, 900, 3600, 900, 4800, 10800, 9000, 720, 1, 84, 252, 420, 1890, 9450, 6300, 9450, 16800, 100800, 50400, 63000, 189000, 90720, 5040, 1, 112, 392, 784, 490, 3528, 21168, 35280, 26460, 35280, 47040, 352800, 235200, 705600, 88200, 294000, 2352000, 1764000, 846720, 3175200, 987840, 40320, 1, 144, 576, 1344, 2016, 6048, 42336

Offset: 1

Author

Alford Arnold, Oct 22 2010

Keywords

• nonn
• tabf

Comments

This is a refinement of the triangle A048743.

Row n has A000041(n) elements.

The sequence can be derived by expanding A007318 and A000142 and using A036040.

For example, row four can be derived using

(1 3 3 3 1) times (1 2 2 6 24) times (1 4 3 6 1) = (1 24 18 108 24)

Examples

			The table begins:
1
1...2
1..12...6
1..24..18..108..24
		

Crossrefs

Cf. A045531 (row sums), A048743, A007318, A036040.

Extensions

Row 6 onwards and definition by R. J. Mathar, Feb 12 2013