A178190 Sum 7^((k^2+3k)/2) from k=1 to n.

49, 16856, 40370463, 678263443312, 79792944561055313, 65712442156478841194856, 378818757978106938161558820799, 15286701010761334171872123930835647200

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..40

Crossrefs

Cf. A178184-A178193.

Programs

Maple

A178190:=n->add(7^((k^2 + 3*k)/2), k=1..n); seq(A178190(n), n=1..10); # Wesley Ivan Hurt, Apr 01 2014

Mathematica

aa = {}; m = 7; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, sum], {n, 1, 20}]; aa (* Artur Jasinski *)
Table[Sum[7^((k^2 + 3 k)/2), {k, n}], {n, 10}] (* Wesley Ivan Hurt, Apr 01 2014 *)

PARI

a(n) = sum(k=1, n, 7^((k^2+3*k)/2)); \\ Michel Marcus, Sep 09 2013