login
A059922
Each term in the table is the product of the two terms above it + 1.
6
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 10, 4, 1, 1, 5, 41, 41, 5, 1, 1, 6, 206, 1682, 206, 6, 1, 1, 7, 1237, 346493, 346493, 1237, 7, 1, 1, 8, 8660, 428611842, 120057399050, 428611842, 8660, 8, 1, 1, 9, 69281, 3711778551721, 51458022952549550101, 51458022952549550101, 3711778551721, 69281, 9, 1
OFFSET
0,5
COMMENTS
Row sums are A059731.
FORMULA
a(m, n) = a(m-1, n-1)*a(m-1, n)+1, a(0, 0) = 1, a(m, n) = 0 iff n>m or n<0.
EXAMPLE
Triangle begins:
1;
1,1;
1,2,1;
1,3,3,1;
1,4,10,4,1; ...
MAPLE
aaa := proc(m, n) option remember; if n>m or n<0 then 0; elif m=0 and n=0 then 1; else aaa(m-1, n-1)*aaa(m-1, n)+1; fi; end;
MATHEMATICA
a[0, 0] = 1; a[m_, n_] /; (n > m || n < 0) = 0; a[m_, n_] := a[m, n] = a[m-1, n-1]*a[m-1, n] + 1; Table[a[m, n], {m, 0, 9}, {n, 0, m}] // Flatten (* Jean-François Alcover, Sep 10 2013 *)
PROG
(Haskell)
a059922 n k = a059922_tabl !! n !! k
a059922_flattened = concat a059922_tabl
a059922_tabl = iterate (\rs ->
zipWith (+) (0 : reverse (0 : replicate (length rs - 1) 1))
$ zipWith (*) ([1] ++ rs) (rs ++ [1])) [1]
a059730 n = a059922_tabl !! n !! (n-3)
a059731 n = sum (a059922_tabl !! n)
a059732 n = a059922_tabl !! (2*n) !! n
a059733 n = a059922_tabl !! n !! n `div` 2
-- Reinhard Zumkeller, Jun 22 2011
CROSSREFS
KEYWORD
easy,nice,nonn,tabl
AUTHOR
Fabian Rothelius, Feb 09 2001
EXTENSIONS
More terms from N. J. A. Sloane and Larry Reeves, Feb 09 2001.
Corrected by Jonathan Wellons (wellons(AT)gmail.com), May 24 2008
STATUS
approved