

A134283


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


3



1, 3, 1, 10, 6, 1, 35, 20, 9, 9, 1, 126, 70, 60, 30, 27, 12, 1, 462, 252, 210, 100, 105, 180, 27, 40, 54, 15, 1, 1716, 924, 756, 700, 378, 630, 300, 270, 140, 360, 108, 50, 90, 18, 1, 6435, 3432, 2772, 2520, 1225, 1386, 2268, 2100, 945, 900, 504, 1260, 600, 1080, 81
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OFFSET

1,2


COMMENTS

For the ASt order of partitions see the AbramowitzStegun reference given in A117506.
Partition number array M_0(3); the k=3 member in the family of a generalization of the multinomial number arrays M_0 = M_0(2) = A048996.
The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...].
The s2(3,n,m):=A035324(n,m) numbers (generalized Pascal triangle) are obtained by summing in row n all numbers with the same part number m. In the same manner the s2(2,n,m) = binomial(n1,m1) = A007318(n1,m1) numbers are obtained from the partition array M_0 = A048996.


LINKS

Table of n, a(n) for n=1..59.
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) = m!*Product_{j=1..n} (s2(3,j,1)^e(n,k,j))/e(n,k,j)! with s2(3,n,1) = A035324(n,1) = A001700(n1) and the exponent e(n,k,j) of j in the kth partition of n in the ASt ordering of the partitions of n. Exponents 0 can be omitted due to 0!=1.


EXAMPLE

[1]; [3,1]; [10,6,1]; [35,20,9,9,1]; [126,70,60,30,27,12,1]; ...


CROSSREFS

Cf. A049027 (row sums, also of triangle A035324).
Sequence in context: A132964 A171509 A171505 * A035324 A171814 A091965
Adjacent sequences: A134280 A134281 A134282 * A134284 A134285 A134286


KEYWORD

nonn,easy,tabf


AUTHOR

Wolfdieter Lang, Nov 13 2007


STATUS

approved



