A178191 Numerators of sum (1/7)^((k^2+3k)/2) from k=1 to n.

1, 344, 825945, 13881657616, 1633163136864785, 1344980069223035633256, 7753542448037025041629822057, 312883404805904029979088478768109600, 88381817680515537538446482833052972519290401

Offset: 1

Author

Artur Jasinski, May 21 2010

Keywords

• frac
• 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..45

Crossrefs

Cf. A178184-A178193.

Programs

Mathematica

aa = {}; m = 1/7; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, Numerator[sum]], {n, 1, 20}]; aa (*Artur Jasinski*)
Numerator[Accumulate[Table[(1/7)^((n^2+3n)/2),{n,10}]]] (* Harvey P. Dale, Jul 21 2016 *)

PARI

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