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a(n) = T(n)^n, where T() are the triangular numbers (A000217).
4

%I #25 Sep 08 2022 08:45:11

%S 1,1,9,216,10000,759375,85766121,13492928512,2821109907456,

%T 756680642578125,253295162119140625,103510234140112521216,

%U 50714860157241037295616,29345269354638035222576971

%N a(n) = T(n)^n, where T() are the triangular numbers (A000217).

%H Vincenzo Librandi, <a href="/A085741/b085741.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = ((n*(n+1))/2)^n. - _Vincenzo Librandi_, Sep 14 2011

%e a(3) = T(3)^3 = 6^3 = 216.

%p a:=n->mul(sum(j, j=1..n),k=1..n): seq(a(n), n=0..13); # _Zerinvary Lajos_, Jun 02 2007

%t With[{rnn=Range[20]},Join[{1},First[#]^Last[#]&/@Thread[ {Accumulate[ rnn], rnn}]]] (* _Harvey P. Dale_, Dec 08 2013 *)

%o (PARI) a(n) = (n*(n+1)/2)^n; \\ _Michel Marcus_, Feb 19 2019

%o (Magma) [((n*(n+1))/2)^n: n in [0..20]]; // _Vincenzo Librandi_, Sep 14 2011

%Y Cf. A000217.

%Y Essentially the same as A061718.

%Y Cf. A000312, A062206, A212333.

%K nonn,easy

%O 0,3

%A _Jon Perry_, Jul 21 2003

%E More terms from _Ray Chandler_, Nov 09 2003