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A077012 Triangle in which n-th row contains all possible products of n-1 of the first n natural numbers in ascending order.

%I A077012 #29 Jun 29 2025 02:23:05
%S A077012 1,1,2,2,3,6,6,8,12,24,24,30,40,60,120,120,144,180,240,360,720,720,
%T A077012 840,1008,1260,1680,2520,5040,5040,5760,6720,8064,10080,13440,20160,
%U A077012 40320,40320,45360,51840,60480,72576,90720,120960,181440,362880
%N A077012 Triangle in which n-th row contains all possible products of n-1 of the first n natural numbers in ascending order.
%C A077012 Row products of A137853. - _Mats Granvik_, Jun 24 2009
%F A077012 E.g.f.: -log(1-x)/(1-y*x). - _Vladeta Jovovic_, Feb 07 2003
%F A077012 Sum_{n>=1} Sum_{k=0..n-1} 1/T(n, k) = 3*e/2 (= A196533 / 10). - _Amiram Eldar_, Jun 29 2025
%e A077012 Triangle begins:
%e A077012      1;
%e A077012      1,    2;
%e A077012      2,    3,    6;
%e A077012      6,    8,   12,   24;
%e A077012     24,   30,   40,   60,   120;
%e A077012    120,  144,  180,  240,   360,   720;
%e A077012    720,  840, 1008, 1260,  1680,  2520,  5040;
%e A077012   5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320;
%e A077012   ...
%p A077012 A077012_row := proc(n) local k; seq(n!/(n-k),k=0..n-1) end:
%p A077012 seq(print(A077012_row(n)),n=1..9); # _Peter Luschny_, Mar 21 2011
%t A077012 Flatten[Table[n!/(n-k),{n,10},{k,0,n-1}]] (* _Harvey P. Dale_, Dec 25 2011 *)
%Y A077012 Row sums give A000254.
%Y A077012 Cf. A058298, A078921, A137853, A196533.
%K A077012 nonn,tabl
%O A077012 1,3
%A A077012 _Amarnath Murthy_, Oct 26 2002
%E A077012 More terms from _Sascha Kurz_, Jan 26 2003