cp's OEIS Frontend

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

%I A185826 #24 Oct 26 2024 21:17:42
%S A185826 1,25,3375,1336336,1160290625,1870414552161,5026507568359375,
%T A185826 20882706457600000000,126834469112674289266929,
%U A185826 1078732544346879404306640625,12415028528548173886807771291871,188031682201497672618081000000000000,3661926425131437024691115607984619140625
%N A185826 Sum of the next n natural numbers raised to the n-th power.
%C A185826 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.
%H A185826 Harvey P. Dale, <a href="/A185826/b185826.txt">Table of n, a(n) for n = 1..158</a>
%F A185826 a(n) = A006003(n)^n.
%F A185826 a(n) = ((n + n^3)/2)^n. - _Harvey P. Dale_, Apr 24 2022
%t A185826 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 *)
%o A185826 (Python)
%o A185826 num = 100
%o A185826 n = 0
%o A185826 a = []
%o A185826 for i in range(1, num):
%o A185826     sum = 0
%o A185826     for j in range(1, i+1):
%o A185826         sum = sum + (n+j)
%o A185826     n = n + i
%o A185826     a.append(sum**i)
%Y A185826 Cf. A006003.
%K A185826 nonn
%O A185826 1,2
%A A185826 _Amir H. Farrahi_, Feb 05 2011
%E A185826 Edited by _N. J. A. Sloane_, Feb 05 2011