A134274 A certain partition array in Abramowitz-Stegun order (A-St order), called M_3(5)/M_3.

1, 5, 1, 45, 5, 1, 585, 45, 25, 5, 1, 9945, 585, 225, 45, 25, 5, 1, 208845, 9945, 2925, 2025, 585, 225, 125, 45, 25, 5, 1, 5221125, 208845, 49725, 26325, 9945, 2925, 2025, 1125, 585, 225, 125, 45, 25, 5, 1, 151412625, 5221125, 1044225, 447525, 342225

Offset: 1

Author

Wolfdieter Lang, Nov 13 2007

Keywords

• nonn
• easy
• tabf

Comments

Partition number array M_3(5) = A134273 with each entry divided by the corresponding one of the partition number array M_3 = M_3(1) = A036040; in short M_3(5)/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

			Triangle begins:
  [1];
  [5,1];
  [45,5,1];
  [585,45,25,5,1];
  [9945,585,225,45,25,5,1];
  ...
		

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

Row sums A134276 (also of triangle A134275).

Cf. A134150 (M_3(4)/M_3 array).

Formula

a(n,k) = Product_{j=1..n} S2(5,j,1)^e(n,k,j) with S2(5,n,1) = A049029(n,1) = A007696(n) = (4*n-3)(!^4) (quadruple- or 4-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) = A134273(n,k)/A036040(n,k) (division of partition arrays M_3(5) by M_3).