A069876 a(n) = (k-n+1)^n + (k-n+2)^n + ... + (k-1)^n + k^n, where k = n(n+1)/2.

1, 13, 405, 23058, 2078375, 271739011, 48574262275, 11373936899396, 3377498614484589, 1240006139651007925, 551449374186192949841, 292093390490112799117190, 181694111127303339553250275, 131144830297438122797495823519, 108709456000518111261404495694375

Offset: 1

Author

Amarnath Murthy, Apr 25 2002

Keywords

• nonn

Comments

Sum of next n n-th powers.

Examples

			a(1) = 1^1 = 1; a(2) = 2^2 + 3^2 = 13; a(3) = 4^3 + 5^3 + 6^3 = 405; a(4) = 7^4 + 8^4 + 9^4 + 10^4 = 23058.
		

Crossrefs

Cf. A072474 (for squares), A075664 - A075671 (3rd to 10th powers).

Programs

Mathematica

i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; Table[Sum[i^n, {i, i1, i2}], {n, 20}]

Python

def A069876(n): return sum(((n*(n+1)>>1)-i)**n for i in range(n)) # Chai Wah Wu, Feb 10 2025

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Zak Seidov, Sep 24 2002