A055633 Number of nested algorithms a(m,n) where m is the number of items in a contaminated group and n is the total number of unclassified items (0 <= m <= n) (values read by antidiagonals).

1, 1, 1, 2, 1, 10, 1, 2, 280, 2, 10, 235200, 4, 20, 280, 173859840000, 40, 2800, 235200, 98238542885683200000000, 100, 11200, 65856000, 173859840000, 32169371027674057560745102540800000000000000000, 28000, 1317120000

Offset: 1

Author

James Sellers, Jun 06 2000

Keywords

• easy
• nonn
• tabf

Comments

The subsequence a(0,n) is given in A028580.

Examples

			1; 1; 1 2; 1 10; 1 2 280; 2 10 235200; ...
		

References

• D.-Z. Du and F. K. Hwang, Combinatorial Group Testing and Its Applications, World Scientific, 2nd ed., 2000; p. 35.

Crossrefs

A000108, A028580.

Programs

Maple

with(combinat): n := 10: A := array(0..n, 0..n): for i from 0 to n do for j from 0 to n do A[i,j] := 0: od:od: A[0,0] := 1: A[0,1] := 1: for j from 2 to 10 do A[0,j] := binomial(2*(j+1)-2, j+1 - 1)/(j+1)*product(A[0,a], a=1..j-1) od:
for c from 1 to 10 do for b from 1 to c do A[b,c] := binomial(2*(b)-2, b - 1)/(b)*product(A[0, c-x], x=1..b) od: od: for s from 0 to 10 do for n from s to 0 by -1 do if A[n,s-n]>0 then printf(`%d, `,A[n, s-n]) fi; od:od:

Formula

a(0, 0)=1, a(0, 1)=1, a(0, n) = C(n+1)*product(a(0, i), i=1..n-1) for n >= 2 and a(m, n) = C(m)*product(a(0, n-i), i=1..m) for 1 <= m <= n. Here C(n) equals the Catalan number given by binomial(2n-2, n-1)/n.