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A114329
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Triangle T(n,k) = number of partitions of n-set into lists (cf. A000262) with k lists of size 1.
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1
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1, 0, 1, 2, 0, 1, 6, 6, 0, 1, 36, 24, 12, 0, 1, 240, 180, 60, 20, 0, 1, 1920, 1440, 540, 120, 30, 0, 1, 17640, 13440, 5040, 1260, 210, 42, 0, 1, 183120, 141120, 53760, 13440, 2520, 336, 56, 0, 1, 2116800, 1648080, 635040, 161280, 30240, 4536, 504, 72, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..5150
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FORMULA
| E.g.f.: exp(x/(1-x)+(y-1)*x). More generally, e.g.f. for number of partitions of n-set into lists with k lists of size m is exp(x/(1-x)+(y-1)*x^m).
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EXAMPLE
| Triangle begins:
1
0 1
2 0 1
6 6 0 1
36 24 12 0 1
240 180 60 20 0 1
...
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MAPLE
| t:=taylor(exp(x/(1-x)+(y-1)*x), x, 11):for n from 0 to 10 do for k from 0 to n do printf("%d, ", coeff(n!*coeff(t, x, n), y, k)): od: printf("\n"): od: # Nathaniel Johnston, Apr 27 2011
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CROSSREFS
| Cf. A000262, A052845.
Sequence in context: A085845 A138106 A131689 * A101371 A154974 A078341
Adjacent sequences: A114326 A114327 A114328 * A114330 A114331 A114332
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 06 2006
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