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%I #12 May 11 2023 12:29:41
%S 25,3150,1956275,6105471900,95373537112525,7450675970460940650,
%T 2910390496349340822268775,5684344796471297836309816409400,
%U 55511156915602623492479419714357425025
%N a(n) = Sum_{k=1..n} 5^((k^2+3k)/2).
%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="/A178188/b178188.txt">Table of n, a(n) for n = 1..50</a>
%t aa = {}; m = 5; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, sum], {n, 1, 20}]; aa (*Artur Jasinski*)
%t Table[Sum[5^((k^2+3k)/2),{k,n}],{n,10}] (* _Harvey P. Dale_, Jan 17 2015 *)
%o (PARI) a(n) = sum(k=1, n, 5^((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
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