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 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are A059731. LINKS 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: A283113 A123610 A209631 * 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

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