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The r-th term of the n-th row of the following triangle contains product of r successive numbers in decreasing order beginning from T(n)-T(r-1) where T(n) is the n-th triangular number. 1 3 2 6 20 6 10 72 210 24 15 182 1320 3024 120 ... Sequence contains the triangle by rows.
3

%I #8 Mar 14 2015 10:01:16

%S 1,3,2,6,20,6,10,72,210,24,15,182,1320,3024,120,21,380,4896,32760,

%T 55440,720,28,702,13800,175560,1028160,1235520,5040,36,1190,32736,

%U 657720,7893600,39070080,32432400,40320,45,1892,68880,1974024,38955840

%N The r-th term of the n-th row of the following triangle contains product of r successive numbers in decreasing order beginning from T(n)-T(r-1) where T(n) is the n-th triangular number. 1 3 2 6 20 6 10 72 210 24 15 182 1320 3024 120 ... Sequence contains the triangle by rows.

%C The first term in the n-th row is T(n), the n-th term in the n-th row is n! and the product of terms of the n-th row is {T(n)}!. - _Joshua Zucker_, Dec 14 2005

%e For n = 4 the terms of the 4th row are 10, 9*8, 7*6*5, 4*3*2*1.

%Y Cf. A110769.

%K easy,tabl,nonn

%O 1,2

%A _Amarnath Murthy_, Aug 12 2005

%E More terms from _Joshua Zucker_, Dec 14 2005