A178187 Numerators of sum (1/3)^((k^2+3k)/2) from k=1 to n.

1, 28, 2269, 551368, 401947273, 879058686052, 5767504039187173, 113521782003321126160, 6703347705514109178621841, 1187477935988707898665323267628, 631074461779774914374598062671491949

Offset

1,2

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 = 1/3; sum = 0; Do[sum = sum + m^((n + 3) n/2); AppendTo[aa, Numerator[sum]], {n, 1, 20}]; aa (*Artur Jasinski*)
Accumulate[Table[(1/3)^((k^2+3k)/2), {k, 20}]]//Numerator (* Harvey P. Dale, May 29 2020 *)

Prog

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

Crossrefs

Cf. A178184-A178193.

Cf. A217628 (denominators).

Sequence in context: A276702 A007219 A203751 * A184134 A327294 A281137

Adjacent sequences: A178184 A178185 A178186 * A178188 A178189 A178190

Keyword

frac,nonn

Author

Artur Jasinski, May 21 2010

Status

approved