

A101819


Triangle read by rows: T(n,h) = number of functions f:{1,2,...,n}>{1,2,...,n1} such that Image(f)=h, h=1,2,...,n1, n=2,3,...


5



1, 2, 6, 3, 42, 36, 4, 180, 600, 240, 5, 620, 5400, 7800, 1800, 6, 1890, 36120, 12600, 100800, 15120, 7, 5334, 202860, 1428840, 2646000, 1340640, 141120, 8, 14280, 1016400, 13053600, 46710720, 53343360, 18627840, 1451520, 9, 36792, 4702320
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..38.


FORMULA

T(n, h) = C(n1, h)*U(n, h), where U(n, h) is the array in A019538.


EXAMPLE

First rows:
1
2 6
3 42 36
4 180 600 240
To see that T(4,2)=42, first count 7 functions from {1,2,3,4}
onto {1,2} with f(1)=1 and 7 with f(1)=2. Count 14 onto {1,3}
and 14 onto {2,3}, for a total of 42.


CROSSREFS

Cf. A019538, A101817, A101819, A101821.
Sequence in context: A172031 A111678 A206429 * A177761 A128192 A077750
Adjacent sequences: A101816 A101817 A101818 * A101820 A101821 A101822


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Dec 17 2004


STATUS

approved



