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

0,5

Comments

Row sums are A059731.

Links

Table of n, a(n) for n=0..54.

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

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

Cf. A007318, A059730 - A059733.

Sequence in context: A123610 A209631 A309876 * A229556 A159623 A143199

Adjacent sequences: A059919 A059920 A059921 * A059923 A059924 A059925

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