A178186 Sum 3^((k^2+3k)/2) from k=1 to n.

9, 252, 19935, 4802904, 3491587305, 7629089072292, 50039174188071999, 984820941357799304880, 58150721823981417489695049, 10301109611599361435391036962892, 5474411390529830981438591324606714655

Offset

1,1

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..60

Mathematica

aa = {}; m = 3; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, sum], {n, 1, 20}]; aa (*Artur Jasinski*)
Table[Sum[3^((k^2+3k)/2), {k, n}], {n, 20}] (* Harvey P. Dale, Jul 10 2020 *)
Accumulate[Table[3^((k^2+3k)/2), {k, 15}]] (* Harvey P. Dale, Mar 25 2023 *)

Prog

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

Crossrefs

Cf. A178184-A178193.

Sequence in context: A256019 A135484 A345160 * A348861 A212290 A296950

Adjacent sequences: A178183 A178184 A178185 * A178187 A178188 A178189

Keyword

nonn

Author

Artur Jasinski, May 21 2010

Status

approved