A134133 A certain partition array in Abramowitz-Stegun order (A-St order).

1, 2, 1, 6, 2, 1, 24, 6, 4, 2, 1, 120, 24, 12, 6, 4, 2, 1, 720, 120, 48, 36, 24, 12, 8, 6, 4, 2, 1, 5040, 720, 240, 144, 120, 48, 36, 24, 24, 12, 8, 6, 4, 2, 1, 40320, 5040, 1440, 720, 576, 720, 240, 144, 96, 72, 120, 48, 36, 24, 16, 24, 12, 8, 6, 4, 2, 1, 362880, 40320, 10080

Offset: 1

Author

Wolfdieter Lang, Oct 12 2007

Keywords

• nonn
• easy
• tabf

Comments

The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].

Partition number array M_3(2)= A130561 divided by partition number array M_3 = M_3(1) = A036040.

Examples

			[1], [2,1], [6,2,1], [24,6,4,2,1], [120,24,12,6,4,2,1], ...
		

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Wolfdieter Lang, First 10 rows and more.

Crossrefs

With another ordering of the partitions this becomes A069123.

Cf. A134134 (triangle obtained by summing same m numbers).

Formula

a(n,k) = A130561(n,k)/A036040(n,k) (division of partition arrays M_3(2) by M_3).

a(n,k) = product(j!^e(n,k,j),j=1..n) with the exponent e(n,k,j) of j in the k-th partition of n in the A-St ordering of the partitions of n.