A059922 Each term in the table is the product of the two terms above it + 1.

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

Author

Fabian Rothelius, Feb 09 2001

Keywords

• easy
• nice
• nonn
• tabl

Comments

Row sums are A059731.

Examples

			Triangle begins:
1;
1,1;
1,2,1;
1,3,3,1;
1,4,10,4,1; ...
		

Links

• S. Kak, The Golden Mean and the Physics of Aesthetics

Crossrefs

Cf. A007318, A059730 - A059733.

Programs

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

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 *)

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.

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