A175151 a(n) = Sum_{i=1..n} ((i+1)^i - 1)/i.

1, 5, 26, 182, 1737, 21345, 320938, 5701778, 116812889, 2710555349, 70256770866, 2011763864406, 63066746422417, 2148275748236033, 79009709388692498, 3120334201617871778, 131703367127423550129, 5916556161455825857509, 281857608793034773225930

Offset: 1

Author

Ctibor O. Zizka, Feb 26 2010

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..350

Crossrefs

Cf. A000169, A023037, A037205, A060072.

Programs

Magma

[(&+[((j+1)^j -1)/j: j in [1..n]]): n in [1..30]]; // G. C. Greubel, Aug 16 2022

Mathematica

Accumulate[Table[((i+1)^i-1)/i,{i,20}]] (* Harvey P. Dale, Jul 08 2017 *)

SageMath

[sum(((j+1)^j -1)/j for j in (1..n)) for n in (1..30)] # G. C. Greubel, Aug 16 2022

Formula

a(n) = Sum_{i=1..n+1} A060072(i). - R. J. Mathar, Mar 05 2010

a(n) = Sum_{j=1..n} (j+1)^j/j - H(n), where H(n) is the n-th harmonic number. - G. C. Greubel, Aug 16 2022

Extensions

More terms from R. J. Mathar, Mar 05 2010