A101031 Triangle read by rows: T(n,k) = (1/k) times the number of functions from an n-element set into but not onto a k-element set.

0, 0, 1, 0, 1, 7, 0, 1, 15, 58, 0, 1, 31, 196, 601, 0, 1, 63, 634, 2765, 7656, 0, 1, 127, 1996, 12265, 44136, 116929, 0, 1, 255, 6178, 52925, 248016, 803383, 2092112, 0, 1, 511, 18916, 223801, 1362096, 5432161, 16595776, 43006401, 0, 1, 1023, 57514, 932525

Offset: 0

Author

Clark Kimberling, Nov 26 2004

Keywords

• nonn
• tabl

Examples

			T(3,3) = (1/3)*[ #(functions into) - #(functions onto)] = (3^3 - 6)/3 = 7.
		

Formula

T(n, k) = (A089072(n, k)-A019538(n, k))/k (where the two sequences are indexed as triangular arrays).