A101819 Triangle read by rows: T(n,h) = number of functions f:{1,2,...,n}->{1,2,...,n-1} such that |Image(f)|=h, h=1,2,...,n-1, n=2,3,...

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

Offset

0,2

Links

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

Formula

T(n, h) = C(n-1, 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 A354375

Adjacent sequences: A101816 A101817 A101818 * A101820 A101821 A101822

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 17 2004

Status

approved