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A144279 Partition number array, called M32hat(-3)= 'M32(-3)/M3'= 'A143173/A036040', related to A000369(n,m)= |S2(-3;n,m)| (generalized Stirling triangle). 4
1, 3, 1, 21, 3, 1, 231, 21, 9, 3, 1, 3465, 231, 63, 21, 9, 3, 1, 65835, 3465, 693, 441, 231, 63, 27, 21, 9, 3, 1, 1514205, 65835, 10395, 4851, 3465, 693, 441, 189, 231, 63, 27, 21, 9, 3, 1, 40883535, 1514205, 197505, 72765, 53361, 65835, 10395, 4851, 2079, 1323, 3465 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each partition of n, ordered as in Abramowitz-Stegun (A-St order; for the reference see A134278), is mapped to a nonnegative integer a(n,k) =: M32hat(-3;n,k) with the k-th partition of n in A-St order.

The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].

If M32hat(-3;n,k) is summed over those k with fixed number of parts m one obtains triangle S2hat(-3):= A144280(n,m).

LINKS

Table of n, a(n) for n=1..55.

W. Lang, First 10 rows of the array and more.

W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3.

FORMULA

a(n,k)= product(|S2(-3,j,1)|^e(n,k,j),j=1..n) with |S2(-3,n,1)|= A008545(n-1) = (4*n-5)(!^4) (4-factorials) for n>=2 and 1 if n=1 and 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.

Formally a(n,k)= 'M32(-3)/M3' = 'A143173/A036040' (elementwise division of arrays).

EXAMPLE

a(4,3)= 9 = |S2(-3,2,1)|^2. The relevant partition of 4 is (2^2).

CROSSREFS

A144274 (M32hat(-2) array). A144284 (M32hat(-4) array)

Sequence in context: A024432 A016531 A221365 * A144280 A107717 A143173

Adjacent sequences:  A144276 A144277 A144278 * A144280 A144281 A144282

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang Oct 09 2008

STATUS

approved

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Last modified May 23 05:25 EDT 2019. Contains 323508 sequences. (Running on oeis4.)