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

1,4

Comments

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

References

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

Links

Table of n, a(n) for n=1..27.

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.

Example

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

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:

Crossrefs

A000108, A028580.

Sequence in context: A204432 A139004 A074951 * A105606 A132995 A114692

Adjacent sequences: A055630 A055631 A055632 * A055634 A055635 A055636

Keyword

easy,nonn,tabf

Author

James A. Sellers, Jun 06 2000

Status

approved