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Search: id:A120057
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| A120057 |
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Table T(n,k) = sum over all set partitions of n of number at index k. |
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+0
3
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| 1, 2, 3, 5, 8, 9, 15, 25, 29, 31, 52, 89, 106, 115, 120, 203, 354, 431, 474, 499, 514, 877, 1551, 1923, 2141, 2273, 2355, 2407, 4140, 7403, 9318, 10489, 11224, 11695, 12002, 12205, 21147, 38154, 48635, 55286, 59595, 62434, 64331, 65614, 66491, 115975
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OFFSET
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1,2
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FORMULA
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T(n,k) = sum_{i=1,k} A120058(n,i)*B(n-i+1), where B(n) are the Bell numbers, (A000110).
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EXAMPLE
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The set partitions of 3 are {1,1,1}, {1,1,2}, {1,2,1}, {1,2,2} and {1,2,3}. Summing these componentwise gives the third row: 5,8,9.
Table starts:
1,
2,3,
5,8,9,
15,25,29,31,
52,89,106,115,120,
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CROSSREFS
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Cf. A120058, A120095. First column is A000110. Main diagonal is A087648.".
Sequence in context: A125871 A141399 A104737 this_sequence A099422 A056903 A028770
Adjacent sequences: A120054 A120055 A120056 this_sequence A120058 A120059 A120060
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KEYWORD
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nonn,tabl
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 06 2006, Jun 07 2006
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