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

Author

Alexander Adamchuk, Jun 30 2006

Keywords

• frac
• nonn

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

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

Crossrefs

Cf. A061463, A061464.

Cf. A083648.

Programs

Mathematica

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

Formula

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