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A144285
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Lower triangular array called S2hat(-4) related to partition number array A144284.
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6
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1, 4, 1, 36, 4, 1, 504, 52, 4, 1, 9576, 648, 52, 4, 1, 229824, 12888, 712, 52, 4, 1, 6664896, 286272, 13464, 712, 52, 4, 1, 226606464, 8182944, 299520, 13720, 712, 52, 4, 1, 8837652096, 266366016, 8455392, 301824, 13720, 712, 52, 4, 1, 388856692224, 10191545280, 273091392
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If in the partition array M32khat(-4)= A144284 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-4). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.
The first three columns are A008546, A144339, A144340.
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LINKS
| 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.
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FORMULA
| a(n,m)=sum(product(|S2(-4;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(-4,n,1)|= A011801(n,1) = A008546(n-1) = (5*n-6)(!^5) (5-factorials) for n>=2 and 1 if n=1.
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EXAMPLE
| [1];[4,1];[36,4,1];[504,52,4,1];[9576,648,52,4,1];...
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CROSSREFS
| Row sums A144286.
A144280 (S2hat(-3)), A144342 (S2hat(-5)).
Sequence in context: A075804 A059844 A144284 * A091741 A061036 A144267
Adjacent sequences: A144282 A144283 A144284 * A144286 A144287 A144288
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 09 2008
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