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Search: id:A144275
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| A144275 |
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Lower triangular array called S2hat(-2) related to partition number array A144274. |
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+0
6
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| 1, 2, 1, 10, 2, 1, 80, 14, 2, 1, 880, 100, 14, 2, 1, 12320, 1140, 108, 14, 2, 1, 209440, 14880, 1180, 108, 14, 2, 1, 4188800, 249280, 15400, 1196, 108, 14, 2, 1, 96342400, 4801280, 255400, 15480, 1196, 108, 14, 2, 1, 2504902400, 108574400, 4888960, 256440, 15512
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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If in the partition array M32khat(-2)= A144274 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-2). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.
The first three columns are A008544, A144277, A144278.
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REFERENCES
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W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, preprint Oct 2008.
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LINKS
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W. Lang, First 10 rows of the array and more.
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FORMULA
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a(n,m)=sum(product(|S2(-2;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(-2,n,1)|= A004747(n,1) = A008544(n-1) = (3*n-4)(!^3) (3-factorials) for n>=2 and 1 if n=1.
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EXAMPLE
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[1];[2,1];[10,2,1];[80,14,2,1];[880,100,14,2,1];...
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CROSSREFS
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Row sums A144276.
A144270 (S2hat(-1)).
Sequence in context: A112691 A110169 A144274 this_sequence A011268 A163235 A142963
Adjacent sequences: A144272 A144273 A144274 this_sequence A144276 A144277 A144278
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 09 2008
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