

A134284


A certain partition array in AbramowitzStegun order (ASt order), called M_0(3)/M_0.


2



1, 3, 1, 10, 3, 1, 35, 10, 9, 3, 1, 126, 35, 30, 10, 9, 3, 1, 462, 126, 105, 100, 35, 30, 27, 10, 9, 3, 1, 1716, 462, 378, 350, 126, 105, 100, 90, 35, 30, 27, 10, 9, 3, 1, 6435, 1716, 1386, 1260, 1225, 462, 378, 350, 315, 300, 126, 105, 100, 90, 81, 35, 30, 27, 10, 9, 3, 1
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OFFSET

1,2


COMMENTS

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.
Partition number array M_0(3)= A134283 with each entry divided by the corresponding one of the partition number array M_0 = M_0(2) = A048996; in short M_0(3)/M_0.


LINKS

Table of n, a(n) for n=1..66.
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(3,j,1)^e(n,k,j) with s2(3,n,1) = A035324(n,1) = A001700(n1) = binomial(2*n1,n) 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) = A134283(n,k)/A048996(n,k) (division of partition arrays M_0(3) by M_0).


EXAMPLE

[1]; [3,1]; [10,3,1]; [35,10,9,3,1]; [126,35,30,10,9,3,1]; ...
a(4,3) = 9 = 3^2 because (2^2) is the k=4 partition of n=4 in ASt order and s2(3,2,1)=3.


CROSSREFS

Cf. A134826 (row sums coinciding with those of triangle A134285).
Sequence in context: A135573 A257254 A126953 * A134285 A141811 A291538
Adjacent sequences: A134281 A134282 A134283 * A134285 A134286 A134287


KEYWORD

nonn,easy,tabf


AUTHOR

Wolfdieter Lang, Nov 13 2007


STATUS

approved



