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%I #6 Dec 15 2017 17:36:48
%S 0,3,18,122,2111,12442,40850,113347,202343,233506,332600,435405,
%T 525544,546233,554161,716795,1000334,1016217,1142240,1244630,2240515,
%U 2414603,3103412,3203757,3400440,3413651,3424213,3461244,4430222,5226150
%N Numbers n such that concatenating n and the sum of factorials of the digits of n produces a triangular number.
%e 18 is in the sequence because 1!+8! = 40321 and 1918*1919/2 = 1840321.
%t ctnQ[n_]:=Module[{idn=IntegerDigits[n],c},c=FromDigits[Join[idn, IntegerDigits[ Total[idn!]]]]; IntegerQ[(Sqrt[8c+1]-1)/2]]; Select[ Range[0,5300000],ctnQ] (* _Harvey P. Dale_, Sep 20 2012 *)
%Y Cf. A061602, A109016.
%K base,nonn
%O 1,2
%A _Jason Earls_, Jun 17 2005