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%I #9 Sep 02 2013 14:01:57
%S 1,3,6,120,153,5886,40470,41041,40279800
%N Triangular numbers that are sums of distinct factorials.
%C Factorials 0! and 1! are not considered distinct.
%C A115944(a(n)) > 0; subsequence of A059590. - _Reinhard Zumkeller_, Feb 02 2006
%C If there are any terms beyond 40279800 they must be larger than 48!. - _Jon E. Schoenfield_, Aug 04 2006
%e 1 = T(1) = 1!.
%e 3 = T(2) = 2!+1!.
%e 6 = T(3) = 3!.
%e 120 = T(15) = 5!.
%e 153 = T(17) = 5!+4!+3!+2!+1!.
%e 5886 = T(108) = 7!+6!+5!+3!.
%e 40470 = T(284) = 8!+5!+4!+3!.
%e 41041 = T(286) = 8!+6!+1!.
%e 40279800 = T(8975) = 11!+9!+5!.
%t triQ[n_] := IntegerQ@Sqrt[8n+1]; fac=Reverse@Range[21]!; lst={}; Do[ n = Plus@@(fac*IntegerDigits[k, 2, 21]); If[triQ[n], AppendTo[lst, n]; Print[{n, k}]], {k, 2^21-1}]; Union@lst
%Y Cf. A025494.
%K nonn
%O 1,2
%A _Giovanni Resta_, Jan 27 2006
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