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%I #7 Dec 05 2013 19:55:18
%S 1,13,405,23058,2078375,271739011,48574262275,11373936899396,
%T 3377498614484589,1240006139651007925,551449374186192949841,
%U 292093390490112799117190,181694111127303339553250275
%N a(1) = 1, a(2) = 2^2 + 3^2; a(n) = (k-n+1)^n + (k-n)^n + ....(k-1)^n + k^n, where k = n(n+1)/2.
%C Sum of next n n-th powers.
%e 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.
%t i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; Table[Sum[i^n, {i, i1, i2}], {n, 20}]
%Y Cf. A072474 (s=2), A075664 - A075670 (s=3-10), A075671 (s=n).
%K nonn
%O 1,2
%A _Amarnath Murthy_, Apr 25 2002
%E More terms from Larry Reeves (larryr(AT)acm.org) and _Zak Seidov_, Sep 24 2002