A185826 Sum of the next n natural numbers raised to the n-th power.

1, 25, 3375, 1336336, 1160290625, 1870414552161, 5026507568359375, 20882706457600000000, 126834469112674289266929, 1078732544346879404306640625, 12415028528548173886807771291871, 188031682201497672618081000000000000

Offset

1,2

Comments

Write the natural numbers in groups, with group sizes incremented by one, each time: 1; 2,3; 4,5,6; 7,8,9,10; ... and add the numbers in each group, then take the i-th power for the i-th group to get the i-th entry in the sequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..158

Formula

a(n)=((n+n^3)/2)^n - Harvey P. Dale, Apr 24 2022

Mathematica

Module[{nn=15}, #[[1]]^#[[2]]&/@Thread[{Total/@TakeList[Range[(nn(nn+1))/2], Range[ nn]], Range[nn]}]] (* or *) Table[((n+n^3)/2)^n, {n, 20}] (* Harvey P. Dale, Apr 24 2022 *)

Prog

(Python)
num = 100
n = 0
a = range(num+1)
for i in range(1, num):
....sum = 0
....for j in range(1, i+1):
........sum = sum + (n+j)
....n = n + i
....a[i] = sum**i

Crossrefs

A006003. The n-th entry in this sequence (starting from 1) is equal to the (n+1)-st entry of A006003 to the n-th power

Sequence in context: A178188 A203186 A322249 * A178026 A012748 A337725

Adjacent sequences: A185823 A185824 A185825 * A185827 A185828 A185829

Keyword

nonn

Author

Amir H. Farrahi, Feb 05 2011

Extensions

Edited by N. J. A. Sloane, Feb 05 2011

Status

approved