A358204 Decimal expansion of Sum_{n >= 1} (-1)^(n+1)/(2*n)^n.

4, 4, 1, 8, 9, 5, 1, 6, 3, 3, 6, 5, 2, 1, 8, 3, 0, 7, 1, 9, 0, 3, 2, 1, 3, 0, 5, 6, 2, 0, 7, 0, 8, 6, 3, 7, 8, 7, 4, 7, 9, 9, 2, 8, 4, 7, 4, 3, 6, 9, 4, 8, 0, 4, 7, 7, 8, 3, 7, 8, 7, 0, 3, 9, 0, 7, 0, 7, 0, 5, 1, 7, 0, 5, 5, 7, 1, 7, 6, 2, 6, 4, 8, 7, 3, 1, 5, 9, 2, 1, 2, 7, 7, 0, 3, 4, 2, 6, 0, 9

Offset

0,1

Links

Table of n, a(n) for n=0..99.

M. L. Glasser, A note on Beukers's and related integrals, Amer. Math. Monthly 126(4) (2019), 361-363.

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

Formula

Equals (1/2)*Integral_{x = 0..1} x^(x/2) dx.

Equals (-1/2)*Integral_{x = 0..1} log(x)*(x^(x/2)) dx.

Equals the double integral (1/2)*Integral_{x = 0..1, y = 0..1} (x*y)^(x*y/2) dx dy (apply Glasser, Theorem 1).

Example

0.44189516336521830719032130562070863787479928...

Maple

evalf( add( (-1)^(n+1)/(2*n)^n, n = 1..50), 100);

Mathematica

RealDigits[N[Integrate[x^(x/2), {x, 0, 1}]/2, 120]][[1]] (* Amiram Eldar, Jun 21 2023 *)

Prog

(PARI) suminf(n=1, (-1)^(n+1)/(2*n)^n) \\ Michel Marcus, Nov 03 2022

Crossrefs

Cf. A073009, A098686, A358191, A358203.

Sequence in context: A211788 A318732 A016706 * A138679 A179399 A371401

Adjacent sequences: A358201 A358202 A358203 * A358205 A358206 A358207

Keyword

cons,nonn,easy

Author

Peter Bala, Nov 03 2022

Extensions

a(98)-a(99) corrected by Amiram Eldar, Jun 21 2023

Status

approved