cp's OEIS Frontend

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

%I A059922 #18 Sep 10 2013 03:16:46
%S A059922 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,
%T A059922 7,1237,346493,346493,1237,7,1,1,8,8660,428611842,120057399050,
%U A059922 428611842,8660,8,1,1,9,69281,3711778551721,51458022952549550101,51458022952549550101,3711778551721,69281,9,1
%N A059922 Each term in the table is the product of the two terms above it + 1.
%C A059922 Row sums are A059731.
%H A059922 S. Kak, <a href="http://uk.arXiv.org/abs/physics/0411195">The Golden Mean and the Physics of Aesthetics</a>
%F A059922 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.
%e A059922 Triangle begins:
%e A059922 1;
%e A059922 1,1;
%e A059922 1,2,1;
%e A059922 1,3,3,1;
%e A059922 1,4,10,4,1; ...
%p A059922 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;
%t A059922 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 *)
%o A059922 (Haskell)
%o A059922 a059922 n k = a059922_tabl !! n !! k
%o A059922 a059922_flattened = concat a059922_tabl
%o A059922 a059922_tabl = iterate (\rs ->
%o A059922    zipWith (+) (0 : reverse (0 : replicate (length rs - 1) 1))
%o A059922                $ zipWith (*) ([1] ++ rs) (rs ++ [1])) [1]
%o A059922 a059730 n = a059922_tabl !! n !! (n-3)
%o A059922 a059731 n = sum (a059922_tabl !! n)
%o A059922 a059732 n = a059922_tabl !! (2*n) !! n
%o A059922 a059733 n = a059922_tabl !! n !! n `div` 2
%o A059922 -- _Reinhard Zumkeller_, Jun 22 2011
%Y A059922 Cf. A007318, A059730 - A059733.
%K A059922 easy,nice,nonn,tabl
%O A059922 0,5
%A A059922 _Fabian Rothelius_, Feb 09 2001
%E A059922 More terms from _N. J. A. Sloane_ and Larry Reeves, Feb 09 2001.
%E A059922 Corrected by Jonathan Wellons (wellons(AT)gmail.com), May 24 2008