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%I #19 Dec 23 2017 15:56:09
%S 1,1,2,7,30,149,868,5907,46226,409105,4037904,43954703,522956302,
%T 6749977101,93928268300,1401602636299,22324392524298,378011820620297,
%U 6780385526348296,128425485935180295,2561327494111820294
%N Row sums of triangle A136573.
%C For n > 0, a(n) gives the smallest number requiring n terms to be expressed as a sum of terms in A200748 - _David Eppstein_, Dec 21 2017
%F Row sums of triangle A136573.
%F a(n) = A003422(n+1) + A000142(n+1) - (n+1).
%F a(n) = n!*(n+1) + the sum of the first (n+1) terms of A033312: (0, 0, 1, 5, 23, 119, 719, ...), where A033312 = (k! - 1, k=0,1,2,...).
%F a(n) = a(n-1) + n! - 1. - _David Eppstein_, Dec 21 2017
%e a(4) = 149 = 4!*(5) = 120 + the sum of the first five terms of A033312: (0, 0, 1, 5, 23) = 29, added to 120 = 149.
%e a(4) = 149 = A003422(5) + A000142(5) - (n+1) = 34 + 120 - 5.
%t s=1;lst={};Do[s+=n!-1;AppendTo[lst, s], {n, 0, 2*4!, 1}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t Fold[Append[#1, #1[[-1]] + #2! - 1] &, {1}, Range[20]] (* _Michael De Vlieger_, Dec 22 2017 *)
%Y Cf. A033312, A136573, A000142.
%K nonn
%O 0,3
%A _Gary W. Adamson_, Jan 07 2008
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008
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