cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A074309 Sum of next n terms of the form i^i.

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%I A074309 #17 Dec 06 2021 04:02:36
%S A074309 4,283,50037,17650540,10405067904,9211817140115,11424093748466841,
%T A074309 18896062057822100616,40192544399240309019728,
%U A074309 106876212200059543898143707,347377340594805599176614321101
%N A074309 Sum of next n terms of the form i^i.
%C A074309 Sum of next n terms of the form i^n is A074209. Sum of first n terms of the form i^n is A031971. Sum of first n terms of the form i^i is A001923.
%H A074309 Seiichi Manyama, <a href="/A074309/b074309.txt">Table of n, a(n) for n = 1..193</a>
%F A074309 a(n) = Sum_{i=n+1..2n} i^i.
%F A074309 a(n) ~ (2*n)^(2*n). - _Vaclav Kotesovec_, Dec 06 2021
%e A074309 a(2) = 283 = 3^3 + 4^4, a(3) = 50037 = 4^4 + 5^5 + 6^6, a(4) = 17650540 = 5^5 + 6^6 + 7^7 + 8^8, a(5) = 10405067904 = 6^6 + 7^7 + 8^8 + 9^9 + 10^10.
%t A074309 Table[Sum[i^i, {i, n+1, 2n}], {n, 20}]
%o A074309 (PARI) a(n) = sum(k=n+1, 2*n, k^k); \\ _Seiichi Manyama_, Dec 05 2021
%Y A074309 Cf. A001923, A031971, A074209.
%K A074309 nonn
%O A074309 1,1
%A A074309 _Zak Seidov_, Sep 22 2002