%I #6 Mar 31 2012 10:30:31
%S 1,1,1,2,1,10,1,2,280,2,10,235200,4,20,280,173859840000,40,2800,
%T 235200,98238542885683200000000,100,11200,65856000,173859840000,
%U 32169371027674057560745102540800000000000000000,28000,1317120000
%N 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).
%C The subsequence a(0,n) is given in A028580.
%D D.-Z. Du and F. K. Hwang, Combinatorial Group Testing and Its Applications, World Scientific, 2nd ed., 2000; p. 35.
%F 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.
%e 1; 1; 1 2; 1 10; 1 2 280; 2 10 235200; ...
%p 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:
%p 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:
%Y A000108, A028580.
%K easy,nonn,tabf
%O 1,4
%A _James A. Sellers_, Jun 06 2000