A136574 Row sums of triangle A136573.

1, 1, 2, 7, 30, 149, 868, 5907, 46226, 409105, 4037904, 43954703, 522956302, 6749977101, 93928268300, 1401602636299, 22324392524298, 378011820620297, 6780385526348296, 128425485935180295, 2561327494111820294

Offset: 0

Author

Gary W. Adamson, Jan 07 2008

Keywords

• nonn

Comments

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

Examples

			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.
a(4) = 149 = A003422(5) + A000142(5) - (n+1) = 34 + 120 - 5.
		

Crossrefs

Cf. A033312, A136573, A000142.

Programs

Mathematica

s=1;lst={};Do[s+=n!-1;AppendTo[lst, s], {n, 0, 2*4!, 1}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Fold[Append[#1, #1[[-1]] + #2! - 1] &, {1}, Range[20]] (* Michael De Vlieger, Dec 22 2017 *)

Formula

Row sums of triangle A136573.

a(n) = A003422(n+1) + A000142(n+1) - (n+1).

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,...).

a(n) = a(n-1) + n! - 1. - David Eppstein, Dec 21 2017

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Nov 08 2008