

A134274


A certain partition array in AbramowitzStegun order (ASt order), called M_3(5)/M_3.


4



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
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OFFSET

1,2


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 ASt order of partitions see the AbramowitzStegun reference given in A117506.


LINKS

Table of n, a(n) for n=1..49.
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.


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*n3)(!^4) (quadruple or 4factorials) and with the exponent e(n,k,j) of j in the kth partition of n in the ASt 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).


EXAMPLE

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


CROSSREFS

Row sums A134276 (also of triangle A134275).
Cf. A134150 (M_3(4)/M_3 array).
Sequence in context: A255979 A269910 A221366 * A134275 A264774 A114154
Adjacent sequences: A134271 A134272 A134273 * A134275 A134276 A134277


KEYWORD

nonn,easy,tabf


AUTHOR

Wolfdieter Lang Nov 13 2007


STATUS

approved



