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A086211
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Triangle related to Bell numbers; T(n,k) read by rows, n>=0, 0<=k<=n: T(n,k) = k*T(n-1,k) + Sum(0<=j, T(n-1,k-1+j)); T(0,0)=1, T(0,k)=0 if k>0.
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3
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1, 1, 1, 2, 3, 1, 6, 9, 6, 1, 22, 31, 28, 10, 1, 92, 123, 126, 69, 15, 1, 426, 549, 586, 418, 145, 21, 1, 2146, 2695, 2892, 2425, 1165, 272, 28, 1, 11624, 14319, 15262, 14058, 8551, 2826, 469, 36, 1
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OFFSET
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0,4
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COMMENTS
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With offset 1 for k, T(n,k) is the number of indecomposable set partitions of [n+2] in which 1 is in the k-th block when the blocks are arranged in order of increasing largest entry. For example, T(2,2)=3 counts 2/134, 23/14, 3/124; see Link. - David Callan, Aug 30 2014
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
1, 1;
2, 3, 1;
6, 9, 6, 1;
22, 31, 28, 10, 1;
92, 123, 126, 69, 15, 1;
426, 549, 586, 418, 145, 21, 1;
2146, 2695, 2892, 2425, 1165, 272, 28, 1;
11624, 14319, 15262, 14058, 8551, 2826, 469, 36, 1 ;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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