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A144356 Partition number array, called M31(6), related to A049374(n,m)= |S1(6;n,m)| (generalized Stirling triangle). 3
1, 6, 1, 42, 18, 1, 336, 168, 108, 36, 1, 3024, 1680, 2520, 420, 540, 60, 1, 30240, 18144, 30240, 17640, 5040, 15120, 3240, 840, 1620, 90, 1, 332640, 211680, 381024, 493920, 63504, 211680, 123480, 158760, 11760, 52920, 22680, 1470, 3780, 126, 1, 3991680, 2661120 (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) =: M31(6;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,...].

Sixth member (K=6) in the family M31(K) of partition number arrays.

If M31(6;n,k) is summed over those k with fixed number of parts m one obtains the unsigned triangle |S1(6)|:= A049374.

LINKS

Table of n, a(n) for n=1..46.

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)=(n!/product(e(n,k,j)!*j!^(e(n,k,j),j=1..n))*product(|S1(6;j,1)|^e(n,k,j),j=1..n)= M3(n,k)*product(|S1(6;j,1)|^e(n,k,j),j=1..n) with |S1(6;n,1)|= A001725(n+4) = (n+4)!/5!, 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. M3(n,k)=A036040.

EXAMPLE

[1];[6,1];[42,18,1];[336,168,108,36,1];[3024,1680,2520,420,540,60,1];...

a(4,3)= 108 = 3*|S1(6;2,1)|^2. The relevant partition of 4 is (2^2).

CROSSREFS

A049402 (row sums).

A144355 (M31(5) array).

Sequence in context: A051338 A062138 A143498 * A049374 A283151 A138192

Adjacent sequences:  A144353 A144354 A144355 * A144357 A144358 A144359

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang Oct 09 2008, Oct 28 2008

STATUS

approved

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Last modified April 19 04:19 EDT 2019. Contains 322237 sequences. (Running on oeis4.)