

A134279


A certain partition array in AbramowitzStegun order (ASt order), called M_3(6)/M_3.


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
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OFFSET

1,2


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


LINKS

Table of n, a(n) for n=1..48.
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(6,j,1)^e(n,k,j) with S2(6,n,1) = A049385(n,1) = A008548(n) = (5*n4)(!^5) (quintuple or 5factorials) 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) = A134278(n,k)/A036040(n,k) (division of partition arrays M_3(6) by M_3).


EXAMPLE

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


CROSSREFS

Row sums give A134281 (also of triangle A134280).
Cf. A134274 (M_3(5)/M_3 partition array).
Sequence in context: A056218 A292219 A197655 * A134280 A134278 A049385
Adjacent sequences: A134276 A134277 A134278 * A134280 A134281 A134282


KEYWORD

nonn,easy,tabf


AUTHOR

Wolfdieter Lang, Nov 13 2007


STATUS

approved



