A134279 A certain partition array in Abramowitz-Stegun order (A-St order), called M_3(6)/M_3.

1, 6, 1, 66, 6, 1, 1056, 66, 36, 6, 1, 22176, 1056, 396, 66, 36, 6, 1, 576576, 22176, 6336, 4356, 1056, 396, 216, 66, 36, 6, 1, 17873856, 576576, 133056, 69696, 22176, 6336, 4356, 2376, 1056, 396, 216, 66, 36, 6, 1, 643458816, 17873856, 3459456, 1463616

Offset: 1

Author

Wolfdieter Lang, Nov 13 2007

Keywords

• nonn
• easy
• tabf

Comments

Partition number array M_3(6) = A134278 with each entry divided by the corresponding one of the partition number array M_3 = M_3(1) = A036040; in short M_3(6)/M_3.

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

For the A-St order of partitions see the Abramowitz-Stegun reference given in A117506.

Examples

			[1]; [6,1]; [66,6,1]; [1056,66,36,6,1]; [22176,1056,396,66,36,6,1]; ...
		

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].
• W. Lang, First 10 rows and more.

Crossrefs

Row sums give A134281 (also of triangle A134280).

Cf. A134274 (M_3(5)/M_3 partition array).

Formula

a(n,k) = Product_{j=1..n} S2(6,j,1)^e(n,k,j) with S2(6,n,1) = A049385(n,1) = A008548(n) = (5*n-4)(!^5) (quintuple- or 5-factorials) and 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.

a(n,k) = A134278(n,k)/A036040(n,k) (division of partition arrays M_3(6) by M_3).