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Search: id:A127136
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| A127136 |
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Triangle read by rows: T(n,k) is the number of endofunctions on n objects with k components. |
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+0
1
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| 1, 2, 1, 4, 2, 1, 9, 7, 2, 1, 20, 17, 7, 2, 1, 51, 48, 21, 7, 2, 1, 125, 127, 60, 21, 7, 2, 1, 329, 352, 174, 65, 21, 7, 2, 1, 862, 963, 504, 190, 65, 21, 7, 2, 1
(list; table; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f. Product_{k=1}^{infinity} 1/(1 - x^k y)^A002861(k).
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EXAMPLE
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For n = 3, the 7 endofunctions are (1,2,3) -> (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,2,3), (1,3,2), and (2,3,1). The components are respectively 123, 123, 13|2, 123, 1|2|3, 1|23, and 123; the number of components is thus 1, 1, 2, 1, 2, 3, 2, 1, so row 3 is 4,2,1.
The triangle starts:
1
2 1
4 2 1
9 7 2 1
20 17 7 2 1
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CROSSREFS
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Cf. A001372 (row sums), A127124, A127125, A002861 (first column).
Adjacent sequences: A127133 A127134 A127135 this_sequence A127137 A127138 A127139
Sequence in context: A060637 A123486 A127124 this_sequence A120025 A109090 A080100
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KEYWORD
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nonn,tabl,more
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 05 2007
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