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%I #12 Mar 25 2023 12:38:18
%S 9,252,19935,4802904,3491587305,7629089072292,50039174188071999,
%T 984820941357799304880,58150721823981417489695049,
%U 10301109611599361435391036962892,5474411390529830981438591324606714655
%N Sum 3^((k^2+3k)/2) from k=1 to n.
%C Series of the kind m^((k^2+3k)/2) from k=1 to n was studied by Bernoulli and Euler.
%H Vincenzo Librandi, <a href="/A178186/b178186.txt">Table of n, a(n) for n = 1..60</a>
%t aa = {}; m = 3; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, sum], {n, 1, 20}]; aa (*Artur Jasinski*)
%t Table[Sum[3^((k^2+3k)/2),{k,n}],{n,20}] (* _Harvey P. Dale_, Jul 10 2020 *)
%t Accumulate[Table[3^((k^2+3k)/2),{k,15}]] (* _Harvey P. Dale_, Mar 25 2023 *)
%o (PARI) a(n) = sum(k=1, n, 3^((k^2+3*k)/2)); \\ _Michel Marcus_, Sep 09 2013
%Y Cf. A178184-A178193.
%K nonn
%O 1,1
%A _Artur Jasinski_, May 21 2010