%I #5 Aug 08 2015 21:56:32
%S 1,1,2,24,25920,1511654400000,11882514930204672000000000000000,
%T 3711388892113415871206624306663300844748800000000000000000000000000000000000
%N Main diagonal of Fibonacci-type array in which each term is equal to the term above multiplied by the term to the left.
%C a(9) has 178 digits. - _R. J. Mathar_, Aug 26 2008
%F T(x, y) = T(x, y-1) * T(x-1, y) T(x, 1) = T(x-2, 1) + T(x-1, 1) T(1, 1) = 1 Direct Formula is T(x, x) for x = {1, 2, 3, 4...}
%e a(4) = T(4,4) = 24; 24 = 2 * 12 = (1 * 2) * (2 * 6) = (1 * 2) * (2 * (2 * 3)) See chart:
%e 1 1 2 3 5 ... (Fibonacci)
%e - 1 2 6 15 T(x, 2)
%e - - 2 12 90 T(x, 3)
%e - - - 24 1080 T(x, 4)
%p A108349T := proc(n,i) option remember ; if n = 1 then combinat[fibonacci](i) ; else procname(n-1,i)*procname(n-1,i+1) ; fi; end: A108349 := proc(n) A108349T(n,1) ; end: for n from 1 to 9 do printf("%d,",A108349(n)) ; od: # _R. J. Mathar_, Aug 26 2008
%K nonn,easy
%O 1,3
%A Brock J Nash (Brocknash(AT)wah.midco.net), Aug 17 2008
%E a(6)-a(8) from _R. J. Mathar_, Aug 26 2008