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A101817
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Triangle read by rows: T(n,h) = number of functions f:{1,2,...,n}->{1,2,...,n} such that |Image(f)|=h; h=1,2,...,n, n=1,2,3,... . Essentially A090657, but without zeros.
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5
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1, 2, 2, 3, 18, 6, 4, 84, 144, 24, 5, 300, 1500, 1200, 120, 6, 930, 10800, 23400, 10800, 720, 7, 2646, 63210, 294000, 352800, 105840, 5040, 8, 7112, 324576, 2857680, 7056000, 5362560, 1128960, 40320, 9, 18360, 1524600, 23496480, 105099120
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = n^n. T(n,1) = n, T(n,n) = n!.
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FORMULA
| T(n, h) = C(n, h)*U(n, h), where U(n, h) is the array in A019538. Thus T(n, h) = C(n, h)*h!*S(n, h), where S(n, h) is a Stirling number of the second kind (given by A048993 with zeros removed).
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EXAMPLE
| First rows:
1;
2, 2;
3, 18, 6;
4, 84, 144, 24;
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MATHEMATICA
| Table[Table[StirlingS2[n, k] Binomial[n, k] k!, {k, 1, n}], {n, 1, 8}] // Grid
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CROSSREFS
| Cf. A090657, A048993, A101818, A101819, A101821.
Sequence in context: A137909 A035796 A049009 * A058159 A058157 A049132
Adjacent sequences: A101814 A101815 A101816 * A101818 A101819 A101820
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Dec 17 2004
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