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%I #6 Jul 05 2013 04:49:15
%S 6,120,210,990,7140,185136,242556,2162160,8239770,258474216,279909630,
%T 9508687656,323015470680,10973017315470,372759573255306,
%U 12662852473364940,430164224521152660,14612920781245825506,496409142337836914550
%N Triangular numbers representable as x!/y! with y < x-1.
%C Triangular numbers in A045619, except A045619(1)=0. The sequence is infinite because A029549 is a subsequence. According to Melissen's comment in A097571, y > x-7.
%C The sequence of x's producing a(n): A227026.
%C a(2) and a(3) have two representations:
%C a(2) = 120 = 5*4*3*2 = 6*5*4.
%C a(3) = 210 = 7*6*5 = 15*14.
%e 990 is in the sequence since 990 = 11!/8! = 11*10*9 is a ratio of factorials and 990 = (44)(44 + 1)/2 is a triangular number.
%Y Cf. A000217, A001219, A029549, A045619, A097571, A227026.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Jun 27 2013