A120264 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^k.

1, 3, 85, 5413, 16922537, 456895999, 376274084904457, 24659496552164597077, 13105067550356276873597957, 40953336089635928267832533257, 11684464736880059106484670339210887010027

Offset

1,2

Comments

Denominator of Sum_{k=1..n} (1/k^k)*(-1)^(k+1) is A061464(n).

Sum_{k>=1} (-1)^(k+1)/k^k = Integral_{x=0..1} x^x dx = 0.7834305107121344... A083648(n) gives its decimal expansion {7, 8, 3, 4, 3, 0, 5, 1, 0, 7, 1, 2, 1, 3, 4, 4, 0, 7, 0, 5, 9, ...}. - Alexander Adamchuk, Aug 21 2006

Links

Table of n, a(n) for n=1..11.

Eric Weisstein's World of Mathematics, Sophomore's Dream.

Formula

a(n) = numerator(Sum_{k=1..n} (1/k^k)*(-1)^(k+1)).

Mathematica

Numerator[Table[Sum[1/k^k*(-1)^(k+1), {k, 1, n}], {n, 1, 20}]]

Crossrefs

Cf. A061463, A061464.

Cf. A083648.

Sequence in context: A056262 A042587 A156879 * A292830 A185142 A279020

Adjacent sequences: A120261 A120262 A120263 * A120265 A120266 A120267

Keyword

frac,nonn

Author

Alexander Adamchuk, Jun 30 2006

Status

approved