A178189 Numerators of sum (1/5)^((k^2+3k)/2) from k=1 to n.

1, 126, 78751, 246096876, 3845263687501, 300411225586015626, 117348134994537353906251, 229195576161205769348146484376, 2238238048449275091290493011484375001

Offset: 1

Author

Artur Jasinski, May 21 2010

Keywords

• nonn
• frac

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 = 1/5; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, Numerator[sum]], {n, 1, 20}]; aa (*Artur Jasinski*)

PARI

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