A178188 a(n) = Sum_{k=1..n} 5^((k^2+3k)/2).

25, 3150, 1956275, 6105471900, 95373537112525, 7450675970460940650, 2910390496349340822268775, 5684344796471297836309816409400, 55511156915602623492479419714357425025

Offset: 1

Author

Artur Jasinski, May 21 2010

Keywords

• nonn

Comments

Series of the kind m^((k^2+3k)/2) from k=1 to n was studied by Bernoulli and Euler.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A178184-A178193.

Programs

Mathematica

aa = {}; m = 5; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, sum], {n, 1, 20}]; aa (*Artur Jasinski*)
Table[Sum[5^((k^2+3k)/2),{k,n}],{n,10}] (* Harvey P. Dale, Jan 17 2015 *)

PARI

a(n) = sum(k=1, n, 5^((k^2+3*k)/2)); \\ Michel Marcus, Sep 09 2013