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

0,3

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

Links

Table of n, a(n) for n=0..20.

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

Example

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.

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 *)

Crossrefs

Cf. A033312, A136573, A000142.

Sequence in context: A193464 A166990 A059578 * A290875 A030836 A030931

Adjacent sequences: A136571 A136572 A136573 * A136575 A136576 A136577

Keyword

nonn

Author

Gary W. Adamson, Jan 07 2008

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Status

approved