A096141 a(n) = sum of n n-th powers starting from n^n.

1, 13, 216, 4578, 119525, 3729451, 135771160, 5658574916, 265921407297, 13918657338925, 803220053336096, 50674352524725590, 3470170166345203477, 256369124879898560271, 20325382637400264402000, 1721352869989716653717768, 155096318841564970416473825, 14814157615194815414927670225

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..351

Formula

a(n) = n! * [x^n] exp(n*x)*(exp(n*x) - 1)/(exp(x) - 1). - Ilya Gutkovskiy, Apr 07 2018

a(n) = HurwitzZeta(-n, n) - HurwitzZeta(-n, 2*n). - Stefano Spezia, Dec 06 2025

Example

a(4) = 4^4 + 5^4 + 6^4 + 7^4 = 4578.

Mathematica

Table[Total[Range[n, 2n-1]^n], {n, 20}] (* Harvey P. Dale, Aug 23 2019 *)

Prog

(PARI) a(n)=sum(k=n, 2*n-1, k^n)

Crossrefs

Cf. A031971.

Sequence in context: A132542 A069989 A140517 * A218475 A294982 A320627

Adjacent sequences: A096138 A096139 A096140 * A096142 A096143 A096144

Keyword

nonn

Author

Amarnath Murthy, Jul 16 2004

Extensions

Extended by Ray Chandler, Jul 17 2004

Status

approved