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A144341 Partition number array, called M32hat(-5)= 'M32(-5)/M3'= 'A144268/A036040', related to A011801(n,m)= |S2(-4;n,m)| (generalized Stirling triangle). 3
1, 5, 1, 55, 5, 1, 935, 55, 25, 5, 1, 21505, 935, 275, 55, 25, 5, 1, 623645, 21505, 4675, 3025, 935, 275, 125, 55, 25, 5, 1, 21827575, 623645, 107525, 51425, 21505, 4675, 3025, 1375, 935, 275, 125, 55, 25, 5, 1, 894930575, 21827575, 3118225, 1182775, 874225, 623645 (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(-5;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(-5;n,k) is summed over those k with fixed number of parts m one obtains triangle S2hat(-5):= A144342(n,m).

LINKS

Table of n, a(n) for n=1..50.

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(-5,j,1)|^e(n,k,j),j=1..n) with |S2(-5,n,1)|= A008543(n-1) = (6*n-7)(!^6) (6-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(-5)/M3' = 'A144268/A036040' (elementwise division of arrays).

EXAMPLE

a(4,3)= 25 = |S2(-5,2,1)|^2. The relevant partition of 4 is (2^2).

CROSSREFS

A144284 (M32hat(-4) array).

Sequence in context: A048897 A049029 A051150 * A144342 A144268 A013988

Adjacent sequences:  A144338 A144339 A144340 * A144342 A144343 A144344

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang Oct 09 2008

STATUS

approved

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Last modified August 11 13:02 EDT 2020. Contains 336428 sequences. (Running on oeis4.)