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A144342 Lower triangular array called S2hat(-5) related to partition number array A144341. 5
1, 5, 1, 55, 5, 1, 935, 80, 5, 1, 21505, 1210, 80, 5, 1, 623645, 29205, 1335, 80, 5, 1, 21827575, 782595, 30580, 1335, 80, 5, 1, 894930575, 27002800, 821095, 31205, 1335, 80, 5, 1, 42061737025, 1058476100, 27963925, 827970, 31205, 1335, 80, 5, 1, 2229272062325, 48782479625 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If in the partition array M32khat(-5)= A144341 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-5). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.

The first three columns are A008543, A144344, A144345.

LINKS

Table of n, a(n) for n=1..47.

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,m)=sum(product(|S2(-5;j,1)|^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S2(-5,n,1)|= A013988(n,1) = A008543(n-1) = (6*n-7)(!^6) (6-factorials) for n>=2 and 1 if n=1.

EXAMPLE

[1];[5,1];[55,5,1];[935,80,5,1];[21505,1210,80,5,1];...

CROSSREFS

Row sums A144343.

A144285 (S2hat(-4)).

Sequence in context: A049029 A051150 A144341 * A144268 A013988 A246006

Adjacent sequences:  A144339 A144340 A144341 * A144343 A144344 A144345

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang Oct 09 2008

STATUS

approved

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Last modified November 20 21:05 EST 2018. Contains 317422 sequences. (Running on oeis4.)