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A046817
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Triangle of generalized Stirling numbers of 2nd kind.
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4
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1, 1, 2, 1, 6, 5, 1, 12, 32, 15, 1, 20, 110, 175, 52, 1, 30, 280, 945, 1012, 203, 1, 42, 595, 3465, 8092, 6230, 877, 1, 56, 1120, 10010, 40992, 70756, 40819, 4140, 1, 72, 1932, 24570, 156072, 479976, 638423, 283944, 21147, 1, 90, 3120, 53550, 487704, 2350950, 5660615, 5971350
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n, k) = Sum_{i=k..n} S2(n, i)*S2(i, k).
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EXAMPLE
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Triangle begins:
k = 0 1 2 3 4 sum
n
1 1 1
2 1 2 3
3 1 6 5 12
4 1 12 32 15 60
5 1 20 110 175 52 358
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MATHEMATICA
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a[n_, k_] = Sum[StirlingS2[n, i]*StirlingS2[i, k], {i, k, n}]; Flatten[Table[a[n, k], {n, 1, 10}, {k, n, 1, -1}]][[1 ;; 53]] (* Jean-François Alcover, Apr 26 2011 *)
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CROSSREFS
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Horizontal mirror triangle is A039810 (matrix square of Stirling2).
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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